Tom English has recommended that we read Dembski and Marks’ paper on their Law of Conservation of Information (not to be confused with the Dembski’s previous LCI from his book No Free Lunch). Dembski also has touted the paper several times, and I too recommend it as a stark display of the the authors’ thinking.
Most people won’t take the time to carefully read a 34-page paper, but I submit that the authors’ core concept of “conservation of information” is very easily understood if we avoid equivocal and misleading terms such as information, search, and target. I’ll illustrate it with a setup borrowed from Joseph Bertrand.
The “Bertrand’s box” scenario is as follows: We’re presented with three small outwardly identical boxes, each containing two coins. One has a two silver coins, one has two gold coins, and one has a silver coin and a gold coin. We’ll call the boxes SS, GG, and SG. We are to randomly choose a box, and then randomly pull a coin from the chosen box.
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I’ll follow Patrick’s lead and offer a few comments on another paper from the Evolutionary Informatics Lab. The paper analyzes Tom Schneider’s ev program, and while there are several problems with the analysis, I’ll focus on the first two sentences of the conclusions:
The success of ev is largely due to active information introduced by the Hamming oracle and from the perceptron structure. It is not due to the evolutionary algorithm used to perform the search.
To explain the authors’ terminology, active information is defined quantitatively as a measure of relative search performance — to say that something provides N bits of active information is to say that it increases the probability of success by a factor of 2N. The Hamming oracle is a function that reports the Hamming distance between the its input and a fixed target. The perceptron structure is another function whose details aren’t important to this post. Figure 1 shows how these three components are connected in an iterative feedback loop.
Winston Ewert, William Dembski, and Robert J. Marks II have made available a paper titled Climbing the Steiner Tree — Sources of Active Information in a Genetic Algorithm for Solving the Euclidean Steiner Tree Problem wherein they claim to have identified sources of “active information” in a genetic algorithm used to find solutions to a Steiner problem. The problem referenced in this paper was originally described by Dave Thomas on the Panda’s Thumb almost six years ago. I developed a GA to solve the problem that Dave posed as a challenge a few weeks later, as did a number of other people.
This paper suffers from numerous flaws, starting with a fundamental mischaracterization of the purpose of Thomas’s solution and including general misunderstanding of genetic algorithms, misapplication of the No Free Lunch theorems, spurious claims about “active information”, and incorrect and unsupported assertions regarding the impact of certain GA implementation details.
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