[Southack]

"It IS mathematically proven and a fundamental theorem that is used in a dozen different technical fields. The only reason I learned it was that it was a necessary mathematical foundation for work I do. You certainly won't find any mathematicians that will refute it."

No, what you are citing is folklore, not science. Nobel Prize winner Illya Prigogine CONCLUSIVELY proved, back in 1987, that the very highest possible levels of order could NOT self-form in a chaotic system. There is a limit in every system as to the maximum level of order that can form naturally from chaos.

That's science. Folklore is that a million monkeys typing on a million keyboards for a million years will produce the collected works of Shakespeare. That's what you're trying to say when you claim that useful software programs can just form on their own in a computer if you leave it on long enough.

[tortoise]

No, what you are citing is folklore, not science. Nobel Prize winner Illya Prigogine CONCLUSIVELY proved, back in 1987, that the very highest possible levels of order could NOT self-form in a chaotic system. There is a limit in every system as to the maximum level of order that can form naturally from chaos.

While I don't like to repeat myself, Prigogine actually agrees with everything I've written. I've actually read his papers and you clearly misunderstand what he wrote. I can't sugar coat the fact that you are just plain wrong on this matter.

Folklore is that a million monkeys typing on a million keyboards for a million years will produce the collected works of Shakespeare.

That wasn't folklore, it was a clever pedestrian description of the theorem. Obviously none of those numbers are literally real nor are monkeys typing a particularly good source of randomness.

That's what you're trying to say when you claim that useful software programs can just form on their own in a computer if you leave it on long enough.

Yes, that is what I'm trying to say. Except that "long enough" means tomorrow or next week or your lifetime or something like that to you. Unfortunately, the universe doesn't run on your schedule and many things take a hell of a lot longer than your or my attention span. I can deal with that fact as long as I can prove mathematically that everything works out eventually in a finite amount of time. Note that for any specific case, it is actually quite possible to calculate approximately how long it would take. The result is never "infinity", though in some cases it might as well be for our purposes as human beings (though as history has proven, some "intractable" problems become tractable far quicker than imagined).