Denyse O’Leary, an advocacy journalist employed by one of the principals of the Center for Evolutionary Informatics, reports that I have essentially retracted the first of my papers on the “no free lunch” theorems for search (1996). What I actually have done in my online copy of the paper, marked “emended and amplified,” is to correct an expository error that Dembski and Marks elevated to “English’s Principle of Conservation of Information” in the first of their publications, “Conservation of Information in Search: Measuring the Cost of Success.” Marks, Dembski, and Ewert have responded, in their new book, by deleting me from the history of “no free lunch.” And the consequence is rather amusing. For now, when explaining conservation of information in terms of no free lunch, they refer over and over to performance.1 It doesn’t take a computer scientist, or even a rocket scientist, to see that they are describing conservation of performance, and calling it conservation of information.
The mathematical results of my paper are correct, though poorly argued. In fact, the theorem I provide is more general than the main theorem of Wolpert and Macready, which was published the following year.2 If you’re going to refer to one of the two theorems as the No Free Lunch Theorem, then it really should be mine. Where I go awry is in the exposition of my results. I mistake a lemma as indicating that conservation of performance in search is due ultimately to conservation of information in search.
The root cause of my error is a failure to recognize that the “no free lunch” theorems actually address sampling, not search. There are two main components of a search, one of which generates a sample of possible solutions to a problem, and the other of which outputs the best solution it can find in the sample. The theorems address the choice of a sampling component, assuming that the solution-seeking component is fixed. My lemma indicates that sampling processes are devoid of information. There is no conservation of something that does not exist in the first place. As everyone knows, if only by reading the news, sampling processes are distinguished by their biases. The performance (utility) of a sampling component in generating a sample of possible solutions for use by the solution-seeking component has nothing to do with information.
Evolutionary informatics is founded on the conflation of evolution and search. The main topic of the book is evolutionary search for a solution to a problem. What I hope you will remember always, after reading this post, is:
The sampling component simulates an evolutionary process in which the “fitness” of a solution is its goodness. (What biologists mean by fitness is not goodness, but instead the expected number of offspring left by an organism, depending on its heritable traits.) The solution-seeking component bears no relation to biological evolution. My lemma says that the evolutionary sampling process gains no information about the fitnesses of unsampled solutions by processing the fitnesses of sampled solutions (and has no information in the first place). Technically, the sample is statistically independent of the fitnesses.
If you remember now what I hope you will remember always, then you will notice that the opening of Chapter 3, “Design Search in Evolution and the Requirement of Intelligence,” is ever so slightly misleading:
Evolution is often modeled by as a [sic] search process. Mutation, survival of the fittest and repopulation are the components of evolutionary search.
Both of the sentences are false. The first is the opposite of the truth. And the problem is not just with this passage. The authors repeatedly conflate scientific modeling of evolution with engineering of an evolutionary search for a solution to a problem. It is vital that they lead readers to misbelieve that the two are the same, because they develop engineering analysis of evolutionary search only for misapplication to models of evolution. Analysis of how well models work, under the unwarranted assumption that modelers do not model, but instead engineer evolutionary searches to solve problems, is an empty accusation of misconduct. The results of such an analysis are not evidence that the assumption holds. Marks et al. write, in the second paragraph of the preface:
Evolutionary models to date point strongly to the necessity of design. Indeed, all current models of evolution require information from an external designer in order to work. All current evolutionary models simply do not work without tapping into an external information source.
Hopefully you see now that they are referring to an evolutionary search as an evolutionary model. It is an evolutionary search for a solution to a problem that performs well (“works”). What they mean by “external information source” is a fitness function. But I established, 21 years ago, that an evolutionary sampling process does not gain information by processing fitnesses. And what sense does it make, when addressing biological evolution, to regard the probabilistic propensity of a (type of) organism to leave offspring as information coming from an external source? The fact of the matter is that Dembski et al. refer to performance as information, and to everything that causes an evolutionary search to perform well as a source of information.3 It is performance that is conserved.
2 Wolpert and Macready first disseminated their theorem in a 1995 technical report, “No Free Lunch Theorems for Search.” I’d already sketched a proof of the theorem in 1994, challenging Aspi Havewala in his thesis defense.
3 From Section 5.5, “Sources of Information in Evolutionary Search” (emphasis added): “Sources of information embedded in any evolutionary search are mined for active information. […] Evolutionary search mines information rather poorly. The sources of information in the fundamental Darwinian evolutionary model include (1) a large population of agents, (2) beneficial mutation, (3) survival of the fittest and (4) initialization.”