More on Marks, Dembski, and No Free Lunch, by Tom English

Tom English has a great post at his blog, Bounded Science, which I have his permission to cross post here:

Bob Marks grossly misunderstands “no free lunch”

And so does Bill Dembski. But it is Marks who, in a “Darwin or Design?” interview, reveals plainly the fallacy at the core of his and Dembski’s notion of “active information.” (He gets going at 7:50. To select a time, it’s best to put the player in full-screen mode. I’ve corrected slips of the tongue in my transcript.)

[The “no free lunch” theorem of Wolpert and Macready] said that with a lack of any knowledge about anything, that one search was as good as any other search. [14:15]And what Wolpert and Macready said was, my goodness, none of these [“search”] algorithms work as well as [better than] any other one, on the average, if you have no idea what you’re doing. And so the question is… and what we’ve done here is, if indeed that is true, and an algorithm works, then that means information has been added to the search. And what we’ve been able to do is take this baseline, that all searches are the same, and we’ve been able to, in cases where searches work, measure the information that is placed into the algorithm in bits. And we have looked at some of the evolutionary algorithms, and we found out that, strikingly, they are not responsible for any creation of information. [14:40]

And according to “no free lunch” theorems, astonishingly, any search, without information about the problem that you’re looking for, will operate at the same level as blind search.” And that’s… It’s a mind-boggling result. [28:10]

Bob has read into the “no free lunch” (NFL) theorem what he believed in the first place, namely that if something works, it must have been designed to do so. Although he gets off to a good start by referring to the subjective state of the practitioner (“with a lack of knowledge,” “if you have no idea what you’re doing”), he errs catastrophically by making a claim about the objective state of affairs (“one search is as good as any other search,” “all searches are the same”).

 

Does your lack of knowledge about a problem imply that all available solution methods (algorithms) work equally well in fact? If you think so, then you’re on par with the Ravenous Bugblatter Beast of Traal, “such a mind-bogglingly stupid animal, it assumes that if you can’t see it, it can’t see you.” Your lack of knowledge implies only that you cannot formally justify a choice of algorithm. There not only may be, but in practice usually will be, huge differences in algorithm performance.

What boggles my mind is that Marks and Dembski did not learn this from Wolpert and Macready (1997), “No Free Lunch Theorems for Optimization.” In Section III-A, the authors observe that “it is certainly true that any class of problems faced by a practitioner will not have a flat prior.” This means that some problems are more likely than others, and their NFL theorems do not hold in fact. So what is the significance of the theorems?

First, if the practitioner has knowledge of problem characteristics but does not incorporate them into the optimization algorithm, then… the NFL theorems establish that there are no formal assurances that the algorithm chosen will be at all effective. Second, while most classes of problems will certainly have some structure which, if known, might be exploitable, the simple existence of that structure does not justify choice of a particular algorithm; that structure must be known and reflected directly in the choice of algorithm to serve as such a justification. [emphasis mine]

So don’t take my word for it that Bob has twisted himself into intellectual contortions with his apologetics. This comes from an article with almost 2600 citations. If memory serves, Marks and Dembski have cited it in all 7 of their publications.

Marks and Dembski believe, astonishingly, that the NFL theorems say that an algorithm outperforms “blind search” only if some entity has exploited problem-specific information in selecting it, when the correct interpretation is that the practitioner is justified in believing that an algorithm outperforms “blind search” only when he or she exploits problem-specific information in selecting it. This leads them to the fallacious conclusion that when a searchsoutperforms blind search, they can measure the problem-specific information that an ostensible “search-forming process” added tosto produce the gain in performance. They silently equate performance with information, and contrive to transform the gain in performance into an expression that looks like gain of Shannon information.

Their name-game depends crucially on making the outcome of a search dichotomous — absolute success (performance of 1) or absolute failure (performance of 0). Then the expected performance of a search is also its probability of success. There is a probabilitypthat blind search solves the problem, and a probabilityps>pthat searchssolves the problem, and the ratiops/pis naturally interpreted as performance gain. But to exhibit the “added information” (information gain), Marks and Dembski perform a gratuitous logarithmic transformation of the performance gain,

I+ = log (ps/p) = log ps−log p = −log p +log ps,

and call it active information. (The last step is silly, of course. Evidently it makes things look more “Shannon information-ish.”) To emphasize, they convert performance into “information” by sticking to a special case in which expected performance is a probability.

Here’s a simple (in)sanity check. Suppose that I have a “pet” algorithm that I run on all problems that come my way. Obviously, there’s no sense in which I add problem-specific information. But Marks and Dembski cherry-pick the cases in which my algorithm outperforms blind search, and, because active information is by definition the degree to which an algorithm outperforms blind search, declare that something really did add information to the algorithm.

Now, a point I’ll treat only briefly is that Marks and Dembski claim that the cases in which my pet algorithm greatly outperforms blind search are exceedingly rare. The fact is that they do not know the distribution of problems arising in the real world, and have no way of saying how rare or common extreme performance is for simple algorithms. In the case of computational search, we know for sure that the distribution of problems diverges fabulously from the uniform. Yet Marks and Dembski carry on about Bernoulli’s Principle of Insufficient Reason, doing their damnedest to avoid admitting that they are yet again insisting that their subjective assignment of uniform probability be taken as objective.

A bit of irony for dessert [35:50]:

Question: Are you getting any kind of response from the other side? Are they saying this is kind of interesting, or are they kind of putting stoppers in their ears? What’s going on?Answer: It’s more of the stoppers in the ears thus far. We have a few responses on blogs, which are unpleasant, and typically personal attacks, so those are to be ignored. We’re waiting for, actually, something substantive in response.

80 thoughts on “More on Marks, Dembski, and No Free Lunch, by Tom English

  1. Umm the algorithm is the information. You don’t add information to it, you already designed it with the information required to solve the problem.

  2. Umm the algorithm is the information. You don’t add information to it, you already designed it with the information required to solve the problem.

    Which problem? You certainly designed an algorithm with information – navigational ‘rules’, if you like. But it has no information about the space it has to navigate. That information is probed, during the course of the ‘search’ of an actual ‘landscape’.

    It is a bit like the child’s game where one is blindfolded and an object is hidden. The algorithm is that the child responds appropriately to shouts of ‘warmer’ and ‘colder’ from its playmates – novel, contextual information, external to the algorithm itself. The data, not the process. A GA can only perform a search if there is a gradient whereby closer approaches give a higher fitness (‘warmer’) than moves in the wrong direction (‘colder’). If there are dozens of objects in the room, all giving similar signals, one could end up at one, but not the ‘optimal’ one – individual jelly beans, not the big bag. So you might include extra algorithmic processes to ‘drift’ the GA out of these local maxima.

    One could argue that the process of birth, death and reproduction forms an algorithm designed in order to solve the problems of life – to keep populations moving towards local optima as they shift, flatten and rise. But that algorithm does not need to be preconfigured with every environment that the process will ever encounter. It has the capacity to probe any, from where it currently sits, and either enter or be rejected by it according to circumstances.

  3. Bob O’H asked:

    “Joe G,

    How much information, though? How do you get the numeric value?”

    olegt said:

    “You count the number of letters in the recipe.” 🙂

    But in which language and from which recipe book? 😀

  4. In response to the original post: Marks and Dembski argue that the NFL predicts that, on average, a genetic algorithm will do as poorly as random search when it is used to model evolution. They then argue that some outside agency must have provided “active information” if it does better than that.

    Any reasonable model of a real biological system has properties that are far from the behavior of almost all of the fitness surfaces envisaged in the NFL theorem. For example, when fitness are randomly assigned to genotypes, a single mutation will bring us to a genotype that is (on average) as bad as we would get if we mutated all of the sites in the genome simultaneously.

    Marks and Dembski do not point out that when genetic algorithms are doing poorly, it is because the fitness surfaces are this rough. That is implicit in their argument but somehow they do not make the point clear. Furthermore they (again, implicitly) assume that the choice among fitness surfaces which comes up with a much smoother one is made by some active agent such as a Designer. They do not discuss whether the smoothness of the surface is instead simply a consequence of the physics and chemistry of life, including the weakness of long-range interactions. In the rough fitness surfaces each small change in the organism effectively destroys it; real chemistry and physics do not work that way.

  5. In order to have a “reasonable model of a real biological system” we first have to understand said system.

    For example we cannot write a GA to evolve a flagellum. That is because we don’t have an understanding on how one can arise in a population that never had one.

  6. Joe Felsenstein,

    DaveScot made a similar point to suggest that this would mean that ID points towards cosmological ID, i.e. the Designer created a universe with the right properties for evolution to occur. I’ve not seen Dembski tackle that argument, and Dave left UD around the same time.

  7. That is a possibility, however it still doesn’t have any evidentiary support- meaning there isn’t anything to tackle…

  8. Which problem?

    The problem the GA was designed to solve.

    The ‘pet GA’ referred to was not designed to solve any particular problem. One has a pre-designed heuristic that one applies to a novel problem, supplied after the program has been written.

    One could even design a GA that actually picked its own ‘problem’. Is it designed to pick the problem it is designed to solve?

  9. I don’t think JoeG really understood what was meant by the “pet GA”. Maybe it would help Joe if he were to think of someone with a rock, who wanders around banging that rock against everything he encouters. On very rare occasions, it will just so happen that banging on something with a rock will have a desirable effect – maybe produce a pleasing tone.

    Does this mean the rock was “designed” to produce a pleasing tone when banged against that particular object? Was making that noise the problem the rock was designed to solve? I’m guessing this is what JoeG is arguing. Strikes me as a bit of a stretch…

  10. Ok, then change this:
    The problem the GA was designed to solve.

    to

    The problems the GA was designed to solve. Was that too difficult for you to do by yourself?

    One could even design a GA that actually picked its own ‘problem’. Is it designed to pick the problem it is designed to solve?

    Yes, you just said it was- I believe that doomed both V’ger and Nomad (Star Trek)

  11. Bob O’H:
    Joe Felsenstein,

    DaveScot made a similar point to suggest that this would mean that ID points towards cosmological ID, i.e. the Designer created a universe with the right properties for evolution to occur. I’ve not seen Dembski tackle that argument, and Dave left UD around the same time.

    Bob, I think Dembski and Marks regard their Search For A Search argument as dealing with this. If the fitness surfaces are smooth, so that from multiple starting points we can reach the same fitness peaks, then they say that the surfaces embody Active Information (by definition). They then think of the Designer as having put that Information there. Even if the smoothness comes from the most basic laws of physics they would say that. In that case you would be making one of those Fine Tuning Of The Universe arguments. You would then be being at most a theistic evolutionist, not a creationist.

    I think they are uncomfortable about having the Designer do her work that far back, but they do intend to establish a principle that information is conserved.

    I suspect that their notion of Active Information will in the end not be useful, but basically I don’t care, because it does not prove that natural selection cannot bring about adaptation. As long as natural selection can put adaptive information into the genome, I don’t care when that “information” came into existence, whether at the beginning of the Universe or right then.

  12. Well ID cares about the arrival, not so much the survival, of the organisms.

    But anyway how can one tell if natural selection was responsible for any given adaptation?

  13. Creodont2,

    To keep things simple, suppose that programs (recipes) are strings of bits. If a program is long, then its length depends relatively little on the language. For languages A and B, there is an A-program that compiles B-programs into equivalent A-programs. The constant length of the B-to-A compiler is an upper bound on the concision you gain by writing a program in B rather than A. That is, if p is a B-program, and c is the compiler, then cp is an equivalent A-program.

    Almost all fitness functions are computed only by ginormous programs. (I’ve just explained why the programming language is practically irrelevant.) For instance, accepting Seth Lloyd’s estimate that the observed universe registers about 2^400 bits, you would have to use 2^54 universes as a “memory” to store the program for a typical function from seven 64-bit arguments to a 64-bit value.

    In computing practice, the bigger and/or slower the program computing a function, the less likely we are to attempt to optimize it. This is why I said in my post that we know that the distribution of problems in the real world diverges fabulously from the uniform. The creationists impute design to the functions, when their properties derive from scarcity of computational resources.

  14. Flint,

    That’s pretty good. I thought about telling him that an algorithm is a number, but expected him to make numbers into products of intelligence. Look at the brief quote of Wolpert and Macready, and you’ll see three references to choice.

    Almost all sampling (“search”) algorithms are so disorderly that it would be absurd to call them designed. Humans cannot comprehend complex algorithms, and thus do not exhibit intelligence when eliminating them from consideration.

  15. Bob O’H,

    DaveScot made a similar point to suggest that this would mean that ID points towards cosmological ID, i.e. the Designer created a universe with the right properties for evolution to occur. I’ve not seen Dembski tackle that argument, and Dave left UD around the same time.

    I asked Dembski about this a few years ago at UD. He replied that while he himself didn’t think Darwinian evolution was adequate to explain the diversity of life, his work with Marks was intended to show that even if Darwinian evolution were true, fitness would necessarily have a teleological origin.

  16. Joe Felsenstein,

    Dover II is much on my mind. I believe that what we really need are simple, not comprehensive, demonstrations that Dembski and Marks are wrong.

    The NFL theorems clearly do not say that “search” (biased sampling, with performance measured on the sample) succeeds only with information. Marks clearly states the contrary, and furthermore explains how his research program depends on his fallacy.

    This invalidates everything Dembski and Marks have done over the past six years, and it worries me that you seem not to read it that way. If they are wrong in their engineering analysis, then they certainly have nothing to say about biology.

    If someone like you is not persuaded, it’s important for me to know why. Do please fill me in.

  17. keiths:
    Bob O’H,

    I asked Dembski about this a few years ago at UD. He replied that while he himself didn’t think Darwinian evolution was adequate to explain the diversity of life, his work with Marks was intended to show that even if Darwinian evolution were true, fitness would necessarily have a teleological origin.

    Good to see you, Keith. I remember that. But how did Dembski and Marks turn the target into something that exists independently of the fitness function? (Methinks I can answer that.) They claim that the NFL theorems “underwrite” active information. But in the NFL analytic framework, the “search” operates on a given function f, and performance is measured on the sample f(x1), f(x2), …, f(xn). The only way to define “hitting the target” is in terms of f(x) values. In computing, we address only f with short programs, and there is no reason to believe that {x | f(x) in T} is uniform on Dom(f).

    Do you see some sense in what they’re doing that I do not?

  18. Joe G,

    Does that mean that if you throw the same algorithm at different problems, it has different amounts of information?

  19. Tom English:
    Joe Felsenstein,

    Dover II is much on my mind. I believe that what we really need are simple, not comprehensive, demonstrations that Dembski and Marks are wrong.

    I agree. My 2007 paper in Reports of the National Center for Scence Education had much the same aims and tried to make the explanations as intuitively clear as possible.

    The NFL theorems clearly do not say that “search” (biased sampling, with performance measured on the sample) succeeds only with information.

    The NFL theorems do not mention information at all, as I am sure you are aware.

    Marks clearly states the contrary, and furthermore explains how his research program depends on his fallacy.

    This invalidates everything Dembski and Marks have done over the past six years, and it worries me that you seem not to read it that way. If they are wrong in their engineering analysis, then they certainly have nothing to say about biology.

    Well, let’s make sure we are consistent with each other here.

    I would say (and have said in my article and subsequent PT posts) that D&M describe the NFL Theorem correctly and then misapply it. They take average behavior over all possible fitness functions (when f(x) is the fitness) and then they implicitly assume that this behavior applies to real-world fitness functions.

    That in turn amounts to the assertion that real-world fitness functions are also typical fitness functions randomly sampled from all possible fitness functions. In those, there would be no correlation between fitness of a parent genotype and an offspring that had undergone a mutation. So in effect one mutation brings the organism to a disastrous state which is just as bad as if all bases in its DNA had mutated smultaneously.

    Where information comes in, AFAIK, is that D&M then say that if the search performs better than on such a “white noise” fitness function, the fitness function must have been chosen from among all possible fitness functions, and they then start saying that “active information” was involved and implying that this could only come from a Designer. That choice by a Designer is their “Search For a Search”.

    I have commented on that by pointing out that ordinary physics may be the reason that fitness functions in real biology do not have the property that one mutation is as bad as totally mutating the organism. If so, no Designer need be invoked.

    Is this consistent with what you are saying? Are you simply focusing on a different part of D&M’s paper? Are you saying something consistent with this?

    I do very much agree that we should thrash this out.

  20. How does the designer traverse the landscape if it is as rugged as ID proponents assert?

  21. Tom, let me jiust add that Wolpert and Macready’s paper does have some discussion of information theory later in the paper, but this is in terms of choosing the search algorithm from among all possible search algorithms. As far as I can see that is different from Dembski and Marks’s Search For A Search, which is about choosing from among all possible fitness functions. The NFL theorems themselves do not talk about information.

  22. Funny, there is a thread about natural selection and no one presented any positive evidence to support it.

    The point being is that starting another thread isn’t going to magically create that evidence that is lacking in the other thread.

  23. Arcane side-remark: Self-replicators exist, and something like the weak anthropic principle applies. I suggest that you start with the constraints that the existence of a self-replicator places on the physics of the environment. It seems to me that an algorithmically random fitness function is a self-contradictory model, tacitly denying the conditions for existence of a self-replicator. Adaptation is a moot issue when there’s nothing that might adapt.

  24. Tom English,

    I am not sophisticated enough to work from the existence of self-replicators and infer from that what kind of physics we have. But people do know about physics, and it is evident that long-range forces are weak. So it is incumbent on Dembski and Marks (not on me) to argue that the existing physics would predispose to “white noise” fitness functions, and that a Teleological Designer is then needed to explain why life can adapt by natural selection.

  25. Dembski has no problem with living organisms adapting via natural selection.

    Intelligent Design has no problem with natural selection…

  26. Joe Felsenstein,

    The concept of objective chance does not apply to the physical universe (perhaps multiverse) in its entirety. (If there were a universe-generating mechanism, it would be part of the universe — a contradiction.) All expressions of improbability of known properties of nature, e.g., the existence of life, are subjective. This is a fundamental reason that arguments from improbability go nowhere. There is no way to turn low subjective probability (ignorance, uncertainty, incredulity) into objective evidence for supernatural intervention.

    I regret having spent a lot of time trying to deconstruct Dembski’s rhetoric. The heart of the matter is that he and Marks are fobbing off subjective probability as objective chance. Irrespective of how they cook the probabilities, the end-product is not objective evidence.

    The folks poring over papers by D&M should look for stuff like “Bernoulli’s principle of insufficient reason therefore applies and we are in our epistemic rights to assume that the probability distribution on Ω is uniform….” D&M always shift to treating the distribution as uniform in fact when they claim that a “search” succeeds only when something has in fact added information.

    My quotation of Marks shows him stitching together subjective and objective interpretations of the main NFL theorems of Wolpert and Macready. I saw this in his first publication with Dembski. But I had to read a couple more papers to be sure.

    (This is not going well, and I need to take a break. Given Elizabeth’s research interests, I’ll mention that I struggle with ADHD-PI. Writing is very hard for me.)

  27. Tom,

    The argument from improbability gives materialism the benefit of the doubt. A benefit it does NOT deserve.

    Also you do not need to deconstruct Dembski’s rhetoric. All you need to do is step up and demonstrate nature, operating freely (no agency involvement) can produce a living organism, a flagellum, a ribosome, etc.

  28. Are we in agreement or not? I have been saying that the man problem with D&M’s argument is that they assume that a smooth fiitness surface needs to be chosen out of all possible fitness surfaces by a Designer, when the laws of physics would predispose to smoothness.

    You identify the problem as that D&M are being subjective about what fitness surfaces are likely a priori. That sounds like almost the same issue. Am I right about your argument? Are we then identifying different problems? Or finding the same problem and describing it differently?

    (Short answers will suffice, thanks for engaging with this).

  29. Joe Felsenstein,

    [Sleep helps. I addressed this last year in a paper I did not manage to finish:] Smoothness does not figure into the theory of D&M. Active information is nothing but a measure of the degree to which an algorithm (to which D&M attach the fitness function) outperforms uniform sampling. It’s crazy to attribute the instantiation of an algorithm to informed choice without inspection of the algorithm. Most algorithms that “hit the target” have algorithmically random decision structures, and are utterly incomprehensible.

    What D&M do in their case studies is to address comprehensible algorithms that others have shown to work, figure out why they worked, and then accuse others of having used information to make them work. Addressing Avida, D&M complain, as Dembski did previously, about the “royal road” to the target in the fitness function. We know that the fitness landscape is not smooth (with respect to the algorithm), because there are long waiting times for steps from one fitness level to the next. I don’t recall that D&M suggested otherwise.

    It occurs to me now that a judge might be impressed by a fat book containing just one incompressible (incomprehensible) algorithm with high active information, along with expert testimony that most algorithms with high active information are fat books. I wonder what rhetoric Dembski would use to brush that away.

  30. I think we’re narrowing in on where we may agree or disagree. True, D&M do not mention smoothness. Most genetic algorithms work by mutation to nearby genotypes (and also recombination, migration, and genetic drift). They get into trouble when the fitness surface is too rough. So the part about roughness is added by me, though in critcisms of Dembski’s use of the NFL Theorem the issue of smoothness versus roughness was raised early on by a number of other people, long before me.

    So I think it is legitimate to raise the issue of where fitness surface smoothness comes from, and to identify D&M’s choice among fitness surfaces as a “choice” that may simply be made by the laws of physics.

    How does this relate to your criticism of D&M?

  31. Tom English: Given Elizabeth’s research interests, I’ll mention that I struggle with ADHD-PI.

    Me too 🙂 Not officially diagnosed (too old) but my Inattention-Memory deficit scores are about 3.5 SDs above the mean.

  32. As you know, almost all fitness functions are algorithmically random. From a computational perspective, they are average-case problems. The probability of obtaining fitness in the upper quantile q with n trials is 1 – (1 – q)^n. For instance, with 1000 trials the probability of obtaining fitness in the top 1% is .99996. As you point out in your (very nice) NCSE paper, the expected fitness for mutation at one locus is the same as for mutations at all loci. A GA would do poorly only if the mutation rate were very low.

    I have to say again that this is all theoretical, because, unless the domain is very small, the typical fitness function has no implementation that fits into the memories of our computers.

    It seems to me that Dembski and Marks are inconsistent in what they say about fitness functions. Sometimes they refer to the “search” as exploiting “search space structure” (that would have to include a fitness function), and in other cases they treat the fitness function as something created to guide the search to the target. The latter is so bizarre that I have trouble responding to it. In engineering applications, there is often embedded in the fitness function a model of a physical system, and fitness is a straightforward measure of how good the response of the system is for the given parameters. And D&M give examples consistent with this.

    I’ve just realized that the inconsistency is probably due to Dembski and Marks saying different things. It’s easy to tell which of them is writing, and I could check that if I could stand going over their papers again.

  33. Tom English:
    As you point out in your (very nice) NCSE paper, the expected fitness for mutation at one locus is the same as for mutations at all loci. A GA would do poorly only if the mutation rate were very low.

    Thanks! Perhaps you meant to say the opposite: I think a GA on a random fitness surface does horribly all the time.

    It seems to me that Dembski and Marks are inconsistent in what they say about fitness functions. Sometimes they refer to the “search” as exploiting “search space structure” (that would have to include a fitness function), and in other cases they treat the fitness function as something created to guide the search to the target. The latter is so bizarre that I have trouble responding to it. In engineering applications, there is often embedded in the fitness function a model of a physical system, and fitness is a straightforward measure of how good the response of the system is for the given parameters. And D&M give examples consistent with this.

    In many engineering applications of GAs, some sort of score is computed for how good the solution is. Then there’s a lot of black arts about how to transform that into fitness to get the best search behavior. In biology that whole level of fussing need not be done: the fitness is the fitness and that’s that. If D&M are being inconsistent about that, it is probably because Marks is thinking of the extra layer of fussing for engineering applications.

  34. An addendum. If I recall correctly, in many engineering GA applications they compute a score, call it “fitness”, and then have some selection procedure that is biased by this “fitness”, but does not choose proportionally to it. For example one could compute a “fitness” and then have the program choose the 10 organisms that have the highest value of that.

    But if people use the word this way that is different from the way biologists use it. Biologists mean by fitness something that is proportional to the probability of surviving and reproducing. In the above example the “fitness” is not the biological fitness, just something computed on the way to getting it. Nonbiological GAs often apply some monotonic function to their “fitness” and then choose proportionally to the resulting value.

    I am raising the possibility that D&M are thinking about the choice of such a monotonic function. If so, they are wasting their time, as a GA that takes a further function like that is not mimicking models of biology.

  35. Joe Felsenstein: Thanks!Perhaps you meant to say the opposite: I think a GA on a random fitness surface does horribly all the time.

    Oops. I meant that it follows from what you said. But I’ve been too breezy. I defined success as obtaining fitness in the upper quantile q, and gave the probability of success when n domain elements are drawn uniformly at random with replacement, p = 1 – (1 – q)^n. I assume that the value of n is small enough that the n elements are distinct with high probability. The probability of success for a GA is approximately p when it evaluates n distinct elements. That statement holds because the distribution of the fitness values does not depend on which elements are evaluated. The expected number of fitness evaluations that a GA actually does (with repeats) to complete n distinct fitness evaluations depends on various factors. When I said that the GA would do well for n = 1000 if the mutation rate were not too low, I was thinking in terms of nontrivial domains (e.g., that of the Weasel problem), typical crossover rates, and typical population sizes.

    You evidently are thinking in terms of time complexity. I’m thinking in terms of NFL analysis, where performance is measured on the sample (no repeats).

    In many engineering applications of GAs, some sort of score is computed for how good the solution is. Then there’s a lot of black arts about how to transform that into fitness to get the best search behavior.

    That’s an example of how the practitioner applies knowledge of the problem. The transformation is part of the algorithm. But we can change the problem (including the measure of performance on the sample) without changing the sampling algorithm. And Dembski and Marks are not entitled to say whenever the algorithm outperforms uniform sampling that the algorithm was designed to achieve that end.

    In biology that whole level of fussing need not be done: the fitness is the fitness and that’s that. If D&M are being inconsistent about that, it is probably because Marks is thinking of the extra layer of fussing for engineering applications.

    So why let them get away with suggesting that something provides the fitness function in order to guide the evolutionary “search” (talk about assuming the conclusion) to the “target” (ditto)? How can you possibly conceive of a target without modeling what you’ve observed with a fitness function?

  36. Regarding your addendum…

    Much of what Dembski and Marks say about computing is bunk because they’re smuggling into the literature their beliefs about biological evolution, and all of what they say about biology is bunk because they assume the conclusion that evolutionary processes are engineered to achieve ends. Given that a major part of their game is to conflate engineering and biology, I think that there should be a fairly clean separation between critiques of their engineering claims and critiques of their biological claims.

  37. Tom English:
    Regarding your addendum…

    Much of what Dembski and Marks say about computing is bunk because they’re smuggling into the literature their beliefs about biological evolution, and all of what they say about biology is bunk because they assume the conclusion that evolutionary processes are engineered to achieve ends. Given that a major part of their game is to conflate engineering and biology, I think that there should be a fairly clean separation between critiques of their engineering claims and critiques of their biological claims.

    Yes, to refute their biological claims all one has to do is demonstrate that blind and undirected chemical processes can actually construct new, useful multi-protein configurations requiring more than two new protein-to-protein binding sites.

    Good luck with that…

  38. Joe G: Yes, to refute their biological claims all one has to do is demonstrate that blind and undirected chemical processes can actually construct new, useful multi-protein configurations requiring more than two new protein-to-protein binding sites.

    Good luck with that…

    Uh, Joe, you might wish to understand the comment you’re responding to, before responding to the voices you hear in your head (once again).

    What do you suppose is the difference between an engineering and a biological claim? Can you tell us in your own words? What do you suppose assuming your conclusions means in this context? Can you tell us in your own words? What do you suppose it might MEAN to separate (human) engineering from evolutionary biology? Can you provide an example in your own words?

    Seriously, knowing what you’re talking about is kind of helpful. Try it for once.

  39. Uh, Flint, you have already proven that you don’t know what you are talking about.

    What do you suppose is the difference between an engineering and a biological claim?

    Why would there be a difference? Biology was engineered.

    What do you suppose assuming your conclusions means in this context?

    It means being an equivocating evolutionist- meaning all evolution is blind watchmaker evolution.

    What do you suppose it might MEAN to separate (human) engineering from evolutionary biology?

    It would eman the continued failure of evolutionary biology.

  40. When D&M start by asserting that biological evolution searches for a target, they can reach no conclusion but that biological evolution is teleological.

    LCI characterizes the information costs that searches incur in outperforming blind search. Searches that operate by Darwinian selection, for instance, often significantly outperform blind search. But when they do, it is because they exploit information supplied by a fitness function — information that is unavailable to blind search. Searches that have a greater probability of success than blind search do not just magically materialize. They form by some process. According to LCI, any such search-forming process must build into the search at least as much information as the search displays in raising the probability of success.

    But who, other than ID creationists, ever said that biological evolution is search? Back in the late 1950’s, people began applying biologically-inspired algorithms to search problems. What’s evident in the quote above is an incredibly stupid assertion that something is using biological processes to solve search problems.

    The only thing that keeps Dembski from being laughed off the face of the planet is his masterful rhetoric. It is quite unfortunate for him that Marks is plain-spoken and unevasive. While Dembski clearly sees the weak points in his arguments, and seeks to conceal them (the less he writes about something, the more scrutiny it deserves), Marks, I think, is honestly wrong.

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