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).
The math does NOT work out in a finite amount of time. Maximum potential order has the maximum potential improbability possible in a chaotic system, per Prigogine.
No, it's folklore. There was actually a demonstration performed about a dozen years ago in which a thousand or so networked computers each simulated a thousand monkeys banging randomingly on keyboards for a thousand years (I don't think that they had the computing power to go to 1MM in time for print back then), and what they were able to show was that pure English words with correct spelling would occassionally be found in the output, but that the words were never in a grammatically correct sentence structure together for anything over 5 words.
They extrapolated from that demonstration that going for the full one million years the monkeys could never produce even one short detective novel, much less a single work by Shakespeare.
I'll do a Google search and see if I can find that old demonstration. It was rather insightful, and aligned very well with Prigogine's new (at that time) points.
"Yes, that is what I'm trying to say." - tortoise
Please click on the link in Post #310 to see why that claim is folklore.
Another way of contemplating the vast impossibility of complex structures forming randomly is to look at a puny 640*480 VGA black and white computer monitor. That screen, with only 307,200 pixels, is capable of displaying EVERY human face on this planet, one at a time. Now imagine running a random program to fill in bits on the screen. Ever think that you'll see the image of a person?!