[Southack]

"The article also makes the (invalid) assumption that each trial takes place in a historical vaccuum; that for each consecutive trial, one sequence is exactly as likely to occur as any other sequence. Feedback mechanisms inherent in natural systems produce a bias that this mathematical model does not address." - Condorman

That's not what the author said. The original scenario that he proposed had data being generated chaoticly. As that data was generated, the author calculated the probability/improbability of 41 characters sequencing in the correct order in any part of that entire data stream. Thus, for the desired result, there is no "historical vaccum" because the entire history of the data is being examined by the math.

As for your comment on "feedback systems", you've got two large hurdles to overcome: First, you have to show that a particular feedback system was in place prior to the very first life form becoming animated, and Second, you've got to demonstrate that such a feedback mechanism could actually change the probability / improbability of useful data self-forming from a chaotic environment.

Frankly, I doubt that either of those two hurdles could be overcome, and even if they were properly managed, would probably not alter the final mathematical result substantially.

Someone also made the flawed comment that the math didn't account for data forming in groups, and then those groups joining with each other, but that too is addressed in the math. To wit: whether you flip four coins at once or one coin at a time, the odds of getting all heads remains precisely the same. So too with data self-forming from a chaotic environment

[Condorman]

you've got two large hurdles to overcome: First, you have to show that a particular feedback system was in place prior to the very first life form becoming animated, and Second, you've got to demonstrate that such a feedback mechanism could actually change the probability / improbability of useful data self-forming from a chaotic environment.

[SCENE: Int. Tent. Spotlight trained on a lone figure in the center ring]

[Condorman prepares to leap two large hurdles in a single bound.]

The crowd goes quiet, a lone child cries and is quickly hushed.

[Drumroll..........]

Condorman: "I give you, The Periodic Table of Elements!!"

[Cymbal crash, trumpet salute]: Ta-da!

The crowd: Whistle, clap, cheer

Condorman: "Thank you, thank you!"

[alarum, fanfare, exunt]

[Condorman]

Someone also made the flawed comment that the math didn't account for data forming in groups, and then those groups joining with each other, but that too is addressed in the math. To wit: whether you flip four coins at once or one coin at a time, the odds of getting all heads remains precisely the same. So too with data self-forming from a chaotic environment

Well that's true as far as your example. But let's say that you flip two coins. Then I flip two coins. Then your boss Bob walks up and flips two coins. Then my good friend Gopal and his wife Jennifer each flip two coins.

You now have 5 sets of 2 coin flips. What is the probability that at least two of those sets are both heads-heads and we can link them up to form a chain of 4 coin flips, each of which is heads? You might also like to consider that last week I flipped a pair of heads, and that set is still available for incorporation.

The math in your article cannot account for such an occurence. It assumes not only that the target chain forms AT ONCE with no intermediate steps, but also that each failed trial is discarded immediately. That is incontrovertible, my friend.