In what appears to be a forthcoming journal article, ID creationists Winston Ewert, William Dembski, and Robert J. Marks II state a formal result, and justify it merely by citing a three-page paper in the proceedings of a symposium. I was already annoyed with the reviewers and the editors for missing a huge defect, and decided to while away the sleepless hours by checking the putative proof in On the Improbability of Algorithmic Specified Complexity.
The formalism and the argument are atrocious. I eventually decided that it would be easier to reformulate what I thought the authors were trying to say, and to see if I could generate my own proof, than to penetrate the slop. It took me about 20 minutes, working directly in LaTeX. Then I decided to provide some explanation that is missing in the paper.
The theorem is correct. As Ewert, Marks, and Dembski put it, "The probability of obtaining an object exhibiting
I should mention that the result probably comes from Ewert's doctoral dissertation, Algorithmic Specified Complexity, still under wraps at Baylor. (I'm guessing that he refrained from plagiarism, this go around.) Evidently Dembski, a mathematician, did not edit the paper.
The following makes more sense if you read Sections I and II of the paper. Those of you with a bit of math under your belts will be amazed by the difference.
The set of all programs
Rewrite the property of string