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.

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Steve Verdon
About Steve Verdon
Steve has a B.A. in Economics from the University of California, Los Angeles and attended graduate school at The George Washington University, leaving school shortly before staring work on his dissertation when his first child was born. He works in the energy industry and prior to that worked at the Bureau of Labor Statistics in the Division of Price Index and Number Research. He joined the staff at OTB in November 2004.


  1. RJN says:

    What are you doing to us, Steve? Do we have to be smart enough to understand NFL theorems to read about ID?

    If so, it is going to shoot it for a lot of us.

  2. Steve Verdon says:

    Well…I wouldn’t say it quite like that, but technically it is the ID guys who are dragging these things in.

    I’d say you don’t have to be able to follow the proofs, just understand the hypotheses and conclusions of the theorems.

  3. floyd says:

    in the real world, there are usually more than two sides to an issue. objective logic says there at least four possibilities in the ID-EVO discussion; #1] they are both completely wrong,#2] they each hold some truth in error,#3]only one holds some truth in error,or #4]one is true while the other is false. since neither side offers a solid comprehensive view,only #4] has no logical merit. i choose #2]until the more truth is revealed.

  4. RJN says:

    My comment above was intended to be somewhat tongue in cheek. Upon rereading it I see that my intent was well disguised.

    William Dembski is on a mission, I think, to develop logical, and mathematical, tools that will show, convincingly, that evolutionary theory cannot be true because there are insufficient upgrading elements available in unguided nature.

    I think he wants to show that the working environment evolutionary theory is in, deep and wide as it is, will always be insufficient; it will always be unable to foster increasingly complex life.

    I suspect that Mark Chu-Carroll�s critique of NFL theorems vs. Dembskl has points of departure from Dembski�s take on the subject that only Bill himself can answer.

  5. Steve Verdon says:


    Dembski’s quest is doomed to failure in that while the mathematics is correct he is ulitmately going up against a strawman. Since he is challenging his fake version of evolution all his theorems are doomed be useless.

    Take for example Dembski’s work with the NFL theorems. None other than David Wolpert has come out and said it was basically garbage. The problem is that the NFL theorems, in their current form, do not apply to real world evolutionary processes. As one commenter once pointed out if reality and mathematics clash, then it is mathematics that is wrong.

    Dembski’s work with the Displacement Theorems is a classic example. His characterization of evolutionary processes in the introduction of the paper is wrong.

    As for Dembski responding, when it is a criticism from somebody who is actually and expert in their field such as David Wolpert, Mark Chu-Carroll, etc. he tends to either ignore them or engage in insults and snide commentary. Nothing of substance.