[Updated 02/02/2011: A Comment on Active Entropy”.]
A recent published peer-reviewed paper entitled “The Search For A Search: Measuring The Information Cost of Higher Level Search” is one of the more interesting mathematical proofs of a type that I am particularly fond of. The authors of the paper, William Dembski and Robert Marks II (from the Discovery Institute and Baylor University, respectively), prove two interrelated mathematical theorems that provide some heft with regards to the No Free Lunch Theorems. I am fond of “No Free Lunch” Theorems as they provide some grounding for the conservation of information necessary to successfully solve the intractable problems of the origin of life.
What this paper does, in a very technical way , is to prove that in order to successfully search for information more effectively than blind chance, one must have information to guide one’s search. There are two different kinds of No Free Lunch Theorems, both of which are proved mathematically in this paper. Horizontal No Free Lunch Theorems prove that no searches without information will be more successful on average than unassisted or blind searches, and that searching with the wrong information will be less effective than blind or unassisted searches. Vertical No Free Lunch Theorems, on the other hand, prove that the length of time for searches for searches in the absence of information increase exponentially in time the further the regress for the search.
The implications of these theorems is massive, even if the language used in the paper is highly technical and accessible largely to those with a fondness for information theory and theoretical mathematics. For one, these theorems demonstrate that many of the supposed “blind” searches that try to model evolutionary behavior in reality have front-loaded information or assisted fitness from the researchers themselves. Evolutionary theorists find themselves in a bind—in order to find any kind of evidence for evolutionary development, even on a trivial scale (like the Urey and Miller origin of life experiments) there must be active intelligence on the part of the researchers stacking the deck in favor of even modest results, including information provided through the design of the experiment or through the order of its operations. This information is smuggled in like a magician engaging in parlor sleight-of-hand tricks, but it can be spotted by the watchful observer.
On the other hand, without such sleight-of-hand, the origin of life or its development through unguided and naturalistic means is hopeless. If the active efforts of intelligent and competent and well-trained scientists can only provide modest examples in favorable environmental settings (hardly a test of the real conditions), then unassisted means are hopeless. By proving rigorously and mathematically that without information on the “target” there can be no better results on average than blind chance, Demski and Marks make naturalistic evolutionary development mathematically impossible, since there is simply not enough time for life to develop unassisted according to scientific knowledge. That is what makes No Free Lunch Theorems so beautiful—it basically limits those who would posit inflationary cosmic resources to solve the information problems of life to two options—cheat or admit defeat. Given the stakes of the Evolution-Intelligent Design debate, defeat is not an option, so we should expect to see a lot of cheating, whether that means the positing of infinite universes or other means.
With a friendly graphical and mathematical approach, this paper on No Free Lunch Theorems ought to be a basic staple of any Intelligent Design-friendly course in mathematical logic, biology, or information theory. Despite its technical language, its conclusions are accessible to others, and I hope that Mr. Dembski is able to continue work on making the conclusion more accessible, as he has written books on No Free Lunch in the past.
In the meantime, though, let us celebrate this particular paper, which was published in the Journal of Advanced Computational Intelligence And Intelligence Informatics, a very appropriate journal for such a technical work on information theory. Having provided a bit of information on the matter, hopefully now a successful search for excellent peer-reviewed papers on Intelligent Design can be a little easier. In the meantime, I am looking for ward to more excellent research to examine.
It appears that my wish for more research to examine did not take long. In a paper responding to the Dembski and Marks paper, a researcher steps into some trouble by attempting to refute without understanding precisely what he is refuting . In seeking to find fault with the use of active entropy, he fails to understand that Dembski and Marks showed that “an informed assisted search will, on average, perform worse than a baseline search.” That this is so ought not to be difficult to understand, even by the modest standard of intellectual capabilities found in origin of life debates.
Why is this so? If one assists a search without active information, on average one will do more harm than good, because one’s assistance will likely be based on incorrect information. The origin of life debates have many useful examples of this phenomenon. For example, the active search for mechanisms for prebiotic evolution, in the development of self-replicating RNA or DNA worlds, is itself an example of an uninformed assisted search, uninformed because it denies the possibility (indeed, requirement) of a designer and assisted because such efforts to show the existence of naturalistic evolution receive covert or open assistance from researchers who attempt to stack the deck in favor of evolution in experiments, like the Urey and Miller experiments.
Unless a search takes place in homogeneous space with active and correct information, imparted by an intelligent being with a target in mind, an assisted search is likely to perform worse on average than a random search because the biases of the uninformed “informer” is likely to get in the way by reducing the target space in an area that excludes what one is looking for, thus making any successful search impossible. As the biological world supplies many such examples of uninformed assisted searches in the origin of life debate, and in the study of such wonders as biological machines, should Dembski and Marks wish to turn their mathematical paper into a sociological examination of the culture of science, they would have overwhelming evidence to apply their conclusions on the No Free Lunch Theorems to the actual behavior and results of biological experiments. Whether they will do so, is, of course, up to them.