The No Free Lunch Theorems Q&A
Mark Chu-Carroll at Good Math, Bad Math has answered several questions regarding the application of the No Free Lunch (NFL) theorems to evolution. It is a very good post that approaches the answers to the questions in a very easy to understand manner. They also highlight why Dembski’s attempt to use the NFL theorems as to why evolutionary theory can’t produce complexity (or in Dembski’s jargon, Complex Specified Information) doesn’t work. One question and answer I like in particular is,
NFL works for operations research tasks; why doesn’t it work for evolution?
Receiving multiple emails with this question surprised the heck out of me. It’s an odd question, one which is both deep and shallow at the same time. I suspect that someone somewhere put folks up to asking this one as a response to my argument, but I have no proof of that. Anyway – on to the answer:
One of the key properties of NFL is that it uses blind fitness functions. That is, the fitness function doesn’t get to change itself depending on what landscape you’re running it on. The fitness function in NFL is also deterministic: for any point in the landscape, looking at where it can go next, it can only choose one path as the best.
Evolution is an adaptational process: modelled as a function, it’s more like the learning functions in Case’s computational learning theory than like the fitness functions in NFL; an evolutionary process doesn’t have a fixed path built in to it; it doesn’t even have a real fitness function built in to it. In effect, an evolutionary process is modifying its fitness function as it goes. The landscape that it traverses gets built into the function, so that the longer it runs, the more adapted to the landscape it gets.
Evolution is also not deterministic: it tries multiple paths. Remember that evolution is working on a species, not on individuals. Within a species, multiple adaptations can occur in different sub-populations. That is effectively trying multiple paths. In fact, that’s exactly how speciation occurs: different subpopulations adapt to the environment in different ways.
Pretty nifty. This right here pretty much tells you why there isn’t much love for ID in the NFL theorems. In evolutionary processes the fitness functions change. In the NFL theorems the fitness functions do not change. This right there means that the conclusions of the NFL theorems don’t necessarily have to follow for evolutionary processes. Also, evolutionary processes within a given species can try several different paths. This also is not part of the hypotheses for the NFL theorems so the conclusions of the NFL theorems are called into question for this reason also. Both together should raise very serious doubts.
There are also several good comments as well.
This one I like,
To put it another way, the organism, and the way in which its genes influence function and fitness, is a part of the fitness landscape. For an organism to successfully evolve, its landscape must be one that is navigable for an evolutionary search. So the valid question is not whether evolution is an efficient algorithm for a randomly selected landscape, but whether landscapes for which evolution is an efficient algorithm exist. Stuart Kauffman has done some interesting simulations with very simple models of gene interdependency, arguing that the requirement that the landscape be “smooth” enough for evolution to navigate it sets some constraints on the complexity of interdependencies.
Basically Dembski’s notion that evolution is impossible because it is not better than blind search which is too unlikely is false. It is false because the landscape(s) in question aren’t any randomly selected landscape from all possible landscapes, but those that are navigable by evolutionary processes. In short the NFL theorems aren’t really applicable.
It is things like this that call ID into doubt for me. It isn’t necessarily the motivations/religious views of the people pushing it so much as that it is just some bad scientific/mathematical work.