Joined: May 2008
I just took another go on Dembski's and Marks's Horizontal No Free Lunch Theorem, as KairosFocus referred to it at UncommonDescent:
On a Wrong Remark in a Paper of Robert J. Marks II and William A Dembski
|Abstract: In their 2010 paper The Search for a Search - Measuring the Information Cost of Higher Level Search, the authors William A. Dembski and Robert J. Marks II present as one of two results their so-called Horizontal No Free Lunch Theorem. One of the consequences of this theorem is their remark: If no information about a search exists, so that the underlying measure is uniform, then, on average, any other assumed measure will result in negative active information, thereby rendering the search performance worse than random search. This is quite surprising, as one would expect in the tradition of the No Free Lunch theorem that the performances are equally good (or bad). Using only very basic elements of probability theory, this essay shows that their remark is wrong - as is their theorem.|
The whole essay can be found here.