Evolution and the NFL theorems

_{Mark

December 30, 2007

Intelligent Design}

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Ronald Meester CLICK HERE FOR THE PAPER Department of Mathematics, VU-University Amsterdam,

“William Dembski (2002) claimed that the NoFreeLunch-theorems from op-
timization theory render Darwinian biological evolution impossible. I
argue that the NFL-theorems should be interpreted not in the sense that the models can be used to draw any conclusion about the real biological evolution (and certainly not about any design inference), but in the sense that it allows us to interpret computer simulations of evolutionary processes. I will argue that we learn very little, if anything at all, about biological evolution from simulations. This position is in stark contrast with certain claims in the literature.”

This paper is wonderful! Will it be published? It vindicates what Prof Dembski has been saying all the time whilst sounding like it does not.

“This does not imply that I defend ID in any way; I would like to emphasise this from the outset.”

I love the main useful quote it is a gem!

“I will argue now that simulations of evolutionary processes only demonstrate good programming skills – not much more. In particular, simulations add very little, if anything at all, to our understanding of “real” evolutionary processes.”

“If one wants to argue that there need not be any design in nature, then it is hardly convincing that one argues by showing how a well-designed algorithm behaves as real life is supposed to do.”

Comments

To all, David Wolpert and I have been acquainted for a number of years. Last summer I contacted him by email and asked him to explain why he had reversed himself on the matter of whether the NFL theorems apply to biological evolution. His response was that the statements in "William Dembski's treatment of the No Free Lunch theorems is written in jello" (quoted in #61) and "Coevolutionary Free Lunches" were both correct. He added a supercilious "What don't you understand?" and said no more. I saw no point in responding. Does anyone here find it obvious that both statements are true?Semiotic 007_{January 3, 2008
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Semiotic(113), DaveScot(115), I hope Semi will stay around for a while because I am learning from his expertise and hope to learn some more. I have no idea who Semi is or what his alleged credentials are, but I find his posts educational, in particular when it comes to nonuniformity and NFL. Please guys, don't get into a quibble but let us keep learning.perlopp_{January 2, 2008
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PaV(116), (2) the distribution is over the set |S|^|V|, which is a combination of both |V| and |S|. First of all, |S|^|V| is not a set, it is a number. The set in question is the set of functions from V to S and there are |S|^|V| such functions. Uniform distribution simply means that we consider all of them to be equally likely which Haggstrom argues is not reasonable in a biological context. As he writes, the uniformity assumption implies that changing a single nucleotide is just as bad or good as rearranging the entire genome. Think of yourself: you have a certain genotype and a certain associated fitness (whatever that means). Now change a single nucleotide in some unimportant locus. Under the uniform distribution, you have as much belief in the function that changes your fitness to 0 as the one that does not change your fitness at all. That's not biologically reasonable. Moreover, there is no reason to claim why that insight would automatically imply design. As I understand it, that sums up Haggstrom's argument.perlopp_{January 2, 2008
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Semiotic 007 #107: If one ignores the objections of Wolpert and English (quoted in 68) and models biological evolution in terms of fitness functions on genotypes, then almost all theoretically- possible fitness functions “contain more information” than the observable universe registers (at most 10^90 bits, according to a paper Dr. Dembski likes to cite). Thus the probability of almost all theoretically- possible fitness functions is zero, contradicting the assumption of a uniform distribution. Two questions: (1) If the probability of almost all theoretically-possible fitness functions is zero, isn't this a problem for Darwinism, and not ID? (2) Instead of a uniform distribution, the fitness function, as you're looking at it, would still be amenable to the Dirac Delta function, which means the fitness function exists, but that it is incredibly thin. Again, isn't this a problem for Darwinism, not ID?PaV_{January 2, 2008
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Semiotic 007: "my best guess is that you simply do not understand the phrase [“competition in a bounded arena”"]. Here is an outstanding paper that...ties [the phrase] to neo-Darwinism... The author, Wirt Atmar, earned a dual Ph.D. in electrical engineering and biology, and very few people are as qualified to comment as he." The paper includes some nice insights. However, in many places, it's the typical Darwinist evolutionary interpretation, without justification of the interpretation. Because of this, statements in the paper regarding "Darwinian evolution" are suspect, if not plainly erroneous. Reading the paper doesn't answer what you meant by "competition in a bounded arena." The term "competition" -- the word I say can only be a metaphor in Darwinian usage -- isn't defined. (What a "bounded arena" is accept as self-evident -- although the term "arena" has connotations that aren't legitimate, either.) Bottom line: The paper doesn't address what I wrote. It's essentially 125 kilobytes of yet more dancing. __________ A quote from the paper:
Simulated evolutionary optimization algorithms [note: earlier in the paper Atmar declares "Darwinian evolution, as a process, is an optimization algorithm"] are normally implemented in the following manner: ... Step 3: The quality of behavioral error is assessed for all members of the population, parent and progeny. One of two conditions is generally implemented: (i) the best N are retained to reproduce in the next generation, or (ii) N of the best are probabilistically retained. In either manner, the population remains size-constrained and ultimately the competitive exclusion of the least appropriate ("least fit") is assured. ... [T]hese few steps [including Step 3] are generally characteristic of all simulated evolutionary procedures.
"Step 3" is the crux of the matter. It would be a simulation of Darwinian (nonteleological) evolution only if the "behavioral error" is assessed using a criterion that has been evolved nonteleologically (without any kind of built-in goal). Otherwise, it's teleological evolution -- by intelligent design. Another quote, same idea:
Genetic algorithms are basically a proper simulation of Darwinian evolution. A population of trials is mutated and the best N are retained at each generation.
This is simply wrong. Again, this would be true only if the "best" are determined by an adaptive landscape that has been evolved nonteleologically. This is not the case for any known useful genetic algorithm.j_{January 2, 2008
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kairos #95: After all this is what allow microevolution. Can anyone definitely say exactly how microevolution works genetically? If you start talking about alleles, just remember that the term, allele, arose before anyone knew about DNA. You're arguing here about the characteristics of NFL theorems based on biology; which is what Haggstrom does. Maybe that's not the best way to do math. perlopp #97: You misunderstand Haggstrom’s argument. The uniform distribution is over the set of fitness functions. First of all, it isn't a uniform distribution over the fitness function for two reasons: (1) Haggstrom doesn't mention fitness functions, he simply introduces a function, f, which, of course MAY be a fitness function; (2) the distribution is over the set |S|^|V|, which is a combination of both |V| and |S|. Second, you say I 'misunderstand' Haggstrom's argument. I suppose this means that you do understand it. Please do us the kindness of presenting Haggstrom's actual argument.PaV_{January 2, 2008
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semiotic This thread relates to the only topic I know a great deal about. No one else with my credentials in NFL is going to field questions here. I have not been attacking ID. Folks should be taking advantage of an opportunity to learn about NFL, not fending off the “evilutionist.” After chastising someone else about appealing to authority you appeal to yourself as an authority. Amazing.DaveScot_{January 2, 2008
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Atom(111), We learned earlier from Semiotic(102) precisely what that range of nonuniform priors is. Is it applicable to evolution? No, the permutation invariance that Semi mentions can hardly hold; swapping nucleotides around does not leave fitness unchanged (if I understand correctly, still hoping for Semi to respond to (103)).perlopp_{January 2, 2008
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DaveScot,
Appeals to authority are generally legitimate when the authority is an acknowledged expert in a relevant field and it is not claimed the expert is infallible.
Appealing to an authority who has reversed himself without explanation, and who declares on his own authority a contradiction of what other researchers argue, is not legitimate.
You should read a little more and write a little less.
Have you read #22?
I have read most of the literature related to the NFL theorems
While some of you here pronounce on an amazing range of topics in which you have neither academic training nor research experience, I do not. This thread relates to the only topic I know a great deal about. No one else with my credentials in NFL is going to field questions here. I have not been attacking ID. Folks should be taking advantage of an opportunity to learn about NFL, not fending off the "evilutionist."Semiotic 007_{January 2, 2008
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Semiotic 007, others, From the Wolpert/McReady paper (1997), I think these paragraphs are relevant to the current discussion:
Since it is certainly true that any class of problems faced by a practitioner will not have a flat prior, what are the practical implications of the NFL theorems when viewed as a statement concerning an algorithm’s performance for nonfixed ? This question is taken up in greater detail in Section IV but we offer a few comments here. First, if the practitioner has knowledge of problem characteristics but does not incorporate them into the optimization algorithm, then P(f) is effectively uniform. (Recall that P(f) can be viewed as a statement concerning the practitioner’s choice of optimization algorithms.) In such a case, 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. In other words, the simple existence of structure per se, absent a specification of that structure, cannot provide a basis for preferring one algorithm over another. Formally, this is established by the existence of NFL-type theorems in which rather than average over specific cost functions , one averages over specific “kinds of structure,” i.e., theorems in which one averages P(d^y of m) | m, a) over distributions P(f). That such theorems hold when one averages over all P(f) means that the indistinguishability of algorithms associated with uniform P(f) is not some pathological, outlier case. Rather, uniform P(f) is a “typical” distribution as far as indistinguishability of algorithms is concerned. The simple fact that the P(f) at hand is nonuniform cannot serve to determine one’s choice of optimization algorithm. Finally, it is important to emphasize that even if one is considering the case where f is not fixed, performing the associated average according to a uniform P(f) is not essential for NFL to hold. NFL can also be demonstrated for a range of nonuniform priors.
Atom_{January 2, 2008
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I have no want, just opined to inform.perlopp_{January 2, 2008
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I have no information. I just want to give my opinion. GloppyGalapagos Finch_{January 2, 2008
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perlopp, What is summed in Theorem 1 is probabilities of obtaining a certain sequence of observed values. A measure of performance of a search algorithm is a function of the sequence of values it obtains. If you define performance as a constant function of value sequences, then the mean performance of all search algorithms is identical for all probability distributions on functions. But this in no way implies that the equality in Theorem 1 holds. Put simply, a performance value conveys less information about a search algorithm's behavior does than does the sequence of values it observes as it executes.Semiotic 007_{January 2, 2008
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Semiotic(106), I have no opinion; just wanted to inform you!perlopp_{January 2, 2008
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semiotic Pointing out that an authority who made an assertion REALLY, REALLY, REALLY is an authority and REALLY, REALLY, REALLY did make the assertion does not legitimize an appeal to authority: Appeals to authority are generally legitimate when the authority is an acknowledged expert in a relevant field and it is not claimed the expert is infallible. You should read a little more and write a little less.DaveScot_{January 2, 2008
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perlopp,
Section 8 in this paper by Haggstrom might be of interest to you.
Synopsis of footnote 19: "If you allow me to depart from past practice, and to make individual fitness a function of not only the individual genotype, but the genotypes of all coexisting organisms, then I can produce an NFL theorem. But I don't really want to show you how, and I don't think you should bother to find out how." To depart from the NFL framework of Wolpert and Macready (i.e., making individual fitness a function of the population rather than the individual), derive a new result, and then call it an NFL theorem would be just a tad impressionistic, don't you think? Haagstrom's remark in the footnote has no bearing on the applicability of the existing NFL framework to biological evolution. Also, Wolpert and Macready's Theorem 2 assumes, loosely speaking, that fitness landscapes in succeeding time steps are uncorrelated. Even if fitness is a hypothetical construct, it is abundantly clear that the only times in which fitness landscapes are not highly correlated are when tsunamis hit, volcanoes erupt, meteors strike, forests burn, etc.Semiotic 007_{January 2, 2008
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Semiotic (last one!), Haggstrom's description of Dembski's argument is that either (a) the fitness function is chosen uniformly, or (b) we must infer design. Haggstrom then points to nature to refute both, and also points out the absurdity in giving the uniform distirbution such a privileged status. His argument sounds pretty strong to me. What do you think?perlopp_{January 2, 2008
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Semiotic, Please see my post 93 in case you missed it. I really think Meester's formulation is equivalent to W&M.perlopp_{January 2, 2008
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Semiotic(102), Thanks! Not sure I quite get it though; are we assuming that the domain of f consists of sequences? For example, if f:S x S --> R, are you saying that we require f and g to have the same probability if they have the property that f(s,t)=g(t,s) for all s,t? What does this permutation invariance imply for the sequence of function values f(v1), f(v2),...? Under the uniform distribution Haggstrom points out that the sequence is i.i.d (which also leads him to point out that this particular NFL theorem is more or less trivial). Sorry for being so inquisitive...maybe you shuold just give a link to the paper... :)perlopp_{January 2, 2008
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perlopp,
Not being an expert on NFLT, I am not aware of any other cases than the uniform distribution.
Wolpert and Macready mention in their coevolutionary "free lunch" article that there is NFL if and only if p(f) = p(f o j) for all functions f and for all permutations j of the domain of functions. This applies to a static, not time-varying, probability distribution function p, so the applicability to biological evolution is dubious from the outset. Fitness functions are hypothetical constructs, so there is no way to ascertain that any particular fitness function f applies to any organism (i.e., that p(f) > 0). But for a wide range of fitness functions f a modeler plausibly invokes (implicitly declaring p(f) > 0), almost all composite functions f o j cannot be realized in the observable universe (i.e., p(f o j) = 0). The generalized NFL theorem does not rescue the notion that there is "no free lunch" when biological evolution is modeled as an optimization process.Semiotic 007_{January 2, 2008
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Semiotic(100), Section 8 in this paper by Haggstrom might be of interest to you.perlopp_{January 2, 2008
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kairos, Pointing out that an authority who made an assertion REALLY, REALLY, REALLY is an authority and REALLY, REALLY, REALLY did make the assertion does not legitimize an appeal to authority:
Are you sure? Really this is not the case. That citation is in a paper that is all dedicated to show how NFLT DO NOT hold in some coevolution cases, precisely when there’s a champion. At the end of this paper Wolpert (who was DIRECTLY involved in the ID controversy in the 90’s) do explicitly state that “in the typical coevolutionary scenarios encountered in biology, where there is no champion, the NFL theorems still hold.”
The theorems still hold? Wolpert and Macready do not provide or cite any argument. The only arguments I have found are that the NFL theorems do not apply to biological evolution. The original NFL theorems assume uniform distributions on functions. If one ignores the objections of Wolpert and English (quoted in 68) and models biological evolution in terms of fitness functions on genotypes, then almost all theoretically- possible fitness functions "contain more information" than the observable universe registers (at most 10^90 bits, according to a paper Dr. Dembski likes to cite). Thus the probability of almost all theoretically- possible fitness functions is zero, contradicting the assumption of a uniform distribution. The upshot is that you have not produced an argument for application of the NFL theorems to biological evolution, and I have just sketched a simple argument against.Semiotic 007_{January 2, 2008
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kairos(98), Not being an expert on NFLT, I am not aware of any other cases than the uniform distribution. Maybe they exist, maybe not, but in order to claim "much too restrictive" you should be able to at least come up with some other example.perlopp_{January 2, 2008
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#96 I haven't said that NFLT holds for fitness functions but that NFLT can (but I would have used "may") also hold for fitness functions chosen according to other distributions. So I haven't claimed that NFLT should hold in general but only that the uniformity condition is too much restrictive. In fact, I meant just what you have said: "NFLT may still hold".kairos_{January 2, 2008
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PaV(90), You misunderstand Haggstrom's argument. The uniform distribution is over the set of fitness functions.perlopp_{January 2, 2008
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kairos(95), It makes no sense to say that NFLT holds "for fitness functions", what you need is to specify the probability distribution according to which the fitness function is chosen. If this distribution is uniform, then NFLT holds. For other distributions, NFLT may still hold but there must be conditions; it does not hold in general.perlopp_{January 2, 2008
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#90 PaV
(7) seems to be no more than an interpretation of what Dembski argues in NFL about blind searches and uniform distributions. What do you see wrong with it.
I mean that condition 7 is too much restrictive to bound what NFLT apply to. While certainly this condition would guarantee that NFLT hold, NFLT can also hold for fittness functions that are characterized by landscapes with some moderate and strict local regularity. After all this is what allow microevolution. In other words, your argument is correct but I simply argued that the criticism to the use of NFLT in biology falls before.kairos_{January 2, 2008
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SChessman -- Sort of like it’s impossible to model every rain drop in a storm, but you can show that the barrel fills up anyway. That's a good analogy. I suspect that since there are engineers involved, the simulations provide useful data and, on some level, corroborate with the real world. The only alternative I can think of is that these simulations are experimental, and have not been applied to real world decisions. But Semiotic has the first-hand experience so I'm curious as to his view. I'd be interested in seeing Gil Dodgen chime in.tribune7_{January 2, 2008
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Semiotic(87), The average is just the sum divided by a constant. The theorem states that two probabilities are equal, computed with the law of total probability when the function f is chosen uniformly. Thus, Meester's formulation is equivalent to W & M.perlopp_{January 2, 2008
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tribune7: "So why do they use these simulations?" I expect that, although the simluation isnot modelled exactly time-wise, in terms of the exact location of individual eddies and features, the general number of and behaviour of these small-scale features as modelled averages out to produce very similar macroscopic values of lift and drag. Sort of like it's impossible to model every rain drop in a storm, but you can show that the barrel fills up anyway.SCheesman_{January 2, 2008
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