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Thank you very much for all your attempts to explain this and for your support of Doctor Stochastic!

I would very much like to “move on” though I will continue to disagree with both of you, not because what you said doesn’t make sense, but because it doesn’t comport with the formulation originally established by Doctor Stochastic.

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.

Way early in this dispute I offered that both a bit string as large as or larger than Shakespeare and also an infinite random bit string would contain Shakespeare – but Doctor Stochastic objected on both, so I went back to his formulation precisely. At post 567 I said:

I understood Doctor Stochastic’s statement to mean something like this:
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.

At post 568, Doctor Stochastic objected:

No, I made a much stronger claim. The string that I constructed, 11011100101110111... (concatenating the integers in binary) will contain the works of Shakespeare somewhere within the string. It's constructive.

I responded at 569:

The way you have described this string it has no length boundary, and thus is infinite. This is the "plenitude" argument Dallaporta speaks to - i.e. everything that can exist, does.

I thought we had peace, but the whole issue was resurrected at 606 when I mentioned this:

Indeed, an infinite binary set will contain all possible combinations. That goes with the concept of infinity. But Kolmogorov Complexity et al cannot be computed unless the Turing Machine halts. IOW, the infinity of chance tells us nothing useful, in particular nothing useful concerning evolution biology.

To which Doctor Stochastic objected as follows:

No. The set (0,0,0,0,0....) will not. It's not as easy as it seems to actually list a set that has all combinations at first glance.

That’s when I gave up trying to agree at 616 and took a very hard, cold look at the precise formulation that started this whole dispute. Along the way, I discovered some interesting things including (a) high auto-correlation which would impact printable/readable results and (b) that the Champernowne number is highly structured, i.e. never random. Hence, my response.

(Lurkers: in addition to the linked Chaitin presentation, this post script research document discusses the difference between Champernowne’s 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 can’t 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.