Evolution and the NFL theorems

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December 30, 2007

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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

kairos(150), From Wikipedia: While chronos is quantitative, kairos has a qualitative nature.perlopp_{January 3, 2008
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#149 "1... A theorem is a theorem. To say that it is “concerning” this, that, or the other bears no relevance to its validity." No. :-) "2....NFL does not hold anywhere near approximately (to which you now seem to agree)." No. :-)kairos_{January 3, 2008
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kairos(148), 1. Yep, irrelevant in the context. A theorem is a theorem. To say that it is "concerning" this, that, or the other bears no relevance to its validity. 2. Your Wikipedia quote states that If the condition for NFL holds approximately, then all algorithms yield approximately the same results over all objective functions. With this I agree. However, in your example the condition for NFL does not hold anywhere near approximately (to which you now seem to agree). 3. Apology accepted! 4. Indeed. :)perlopp_{January 3, 2008
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#144
1. NFLT is a proven true mathematical statement about the equality of two quantities. Your distincion between “pure math” and “computational science” is irrelevant.
Oops. Irrelevant? :-)
2. Your suggested example uses a distribution over fitness functions that cannot be said to be approximately uniform (far from it). If you still believe that it is approximately uniform, please present a good argument.
Uniform? And where did I say so? I said just the opposite for the ezample and argued NFLT (in the real world obviously).
3. Yes, the NFLT as stated by W&M and its consequences. Nothing else. That’s what is being discussed here, as started with the link to Meester’s paper and his references to Haggstrom.
Sorry, but the title of the thread is "Evolution and the NFL theorems"; and Evolution did happen in the real world, not in a world of Platonic ideas.
4. Happy New Year!
Happy (future) |S|^|V| year; in the abstract world obviously :-)kairos_{January 3, 2008
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kairos(143), When you say And in the real world your argument doesn’t hold what argument are you referring to?perlopp_{January 3, 2008
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PaV(142), I'd like to redirect you to my post 137 as you still have not replied. I think your answer to 1. is material to how our discussion will proceed. As for 2., there is no question, just a comment that you may have misunderstood the concept of blind search.perlopp_{January 3, 2008
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PaV(142), Again, that is not Haggstrom's premise. That is the premise of the NFL Theorem.perlopp_{January 3, 2008
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kairos(143), 1. NFLT is a proven true mathematical statement about the equality of two quantities. Your distincion between "pure math" and "computational science" is irrelevant. 2. Your suggested example uses a distribution over fitness functions that cannot be said to be approximately uniform (far from it). If you still believe that it is approximately uniform, please present a good argument. 3. Yes, the NFLT as stated by W&M and its consequences. Nothing else. That's what is being discussed here, as started with the link to Meester's paper and his references to Haggstrom. 4. Happy New Year!perlopp_{January 3, 2008
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#141
In the acronym NFLT, “T” stands for “Theorem” and there is no equivocation as it clearly refers to the result by Wolpert & Macready. Your qualifier “abstract” has no meaning in this context. As for the Wikipedia quote, your suggested example is still very far from “approximately.”
T stands for theorem but it's a theorem concerning computational science not pure Maths. This is meant by the wiki citation about which I think you should think more. Concerning the last sentence I don't see how you can reasonably say that my example "is still very far from approximately" after I have proved that from a computational point of view (that is what actually matters in function optimization) |S|^(-2|V|) (|S|^-|V|)/k do both denote unreachable points.
I have no idea whether Dembski has been misunderstood in the way you claim but unless this discussion is going to be about the NFL Theorem by Wolpert & Macready and its consequences, I have nothing to add.
That's your choice but by saying "and its consequences" you have constrained yourself to discuss the consequences of NFLT where they are significant for the problem we are discussing, i.e. in the real world. And in the real world your argument doesn't hold.kairos_{January 3, 2008
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perlopp #138: You say that I go wrong when I say this: “Haggstrom’s premise is that if one or two nucleotides of a genome change, then the fitness for that genome falls to zero.” Here’s Haggstrom’s footnote #11 (which I've taken from my post #55): “In the hypothetical scenario that we had strong empirical evidence for the claim that the true fitness landscape looks like a typical specimen from the model (7), then this evidence would in particular (as argued in the next few paragraphs) indicate that an extremely small fraction of genomes at one or a few mutations’ distance from a genome with high fitness would themselves exhibit high fitness. It is hard to envision how the Darwinian algorithm A could possibly work in such a fitness landscape.” How is this any different from saying that one or two mutations away from a given high fitness genome, you’ll NOT find high fitness. When he says that, at a distance of only one or two mutations away, you’ll only find an “extremely small fraction” of high fitness genomes, this means that it is nearly zero. How else do you define an “extremely small fraction”? You know, 1/10^150 is an “extremely small fraction”. Have you perhaps misunderstood what Haggstrom is saying?PaV_{January 3, 2008
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kairos(140), In the acronym NFLT, "T" stands for "Theorem" and there is no equivocation as it clearly refers to the result by Wolpert & Macready. Your qualifier "abstract" has no meaning in this context. As for the Wikipedia quote, your suggested example is still very far from "approximately." I have no idea whether Dembski has been misunderstood in the way you claim but unless this discussion is going to be about the NFL Theorem by Wolpert & Macready and its consequences, I have nothing to add.perlopp_{January 3, 2008
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#134
The NFLT says that the probability of any particular sample is the same regardless of algorithm. In your example, compare blind search to adjacent-point search with the first point chosen randomly in each case. Now consider a sample of two consecutive high fitness values (”out of the flat landsacpe”). With blind search you must find such a value twice. By independence, the probability is p^2 for some very small p. With adjacent-point search, you need to find it once which has probability p but the conditional probability in the next step is much higher than p; thus beating blind search.
There's an equivication here. I'm not speaking about abstract NFLT; you forgot that from this point of view no NFLT would actually exist in the world; as clearly stated in wikipedia: "NFL is physically possible, but in reality objective functions arise despite the impossibility of their permutations, and thus there is not NFL in the world. The obvious interpretation of "not NFL" is "free lunch," but this is misleading. NFL is a matter of degree, not an all-or-nothing proposition. If the condition for NFL holds approximately, then all algorithms yield approximately the same results over all objective functions." It's just this matter of degree that we are addressing and in this sense your argument, although correct in theory, doesn't hold in practice. In fact, you have correctly stated that in one case we have p^2 and in the other one something like p/k (with k being a integer whose value depends on the number of neighbors). However the value of p is a depressing |S|^-|V|, something that can easily be less than 10^-1000000. In the real world that's no difference between p^2 and p/k. IMHO it's here that the argument of Dembski has been really misunderstood.kairos_{January 3, 2008
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Also in reference to the above speculative mathematics- i remind you all that the subejects they you are trying to apply NFL to are infact no fully understood. NFl is as it stands right now a philosophical argument against evolution without a guiding intelligence. It is in the process of being aplied in the ID research. I think the theory is still just a theory- and one i might ad that has not be disproven. But to me it is an absolutly beautiful revelation about intelligence and its inextricable link to naturalistic origins.Frost122585_{January 3, 2008
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PaV(135), I re-read your post and think I've found the source of your misunderstanding. You write Haggstrom’s premise is that if one or two nucleotides of a genome change, then the fitness for that genome falls to zero. That is not his premise; it is what follows from the premise in the NFL Theorem. What Haggstrom actually writes is that the NFL premise means that "changing a single nucleotide is just as bad as putting togehter a new genome from scratch and completely at random." Again, he does not say that this is the case but that this is an obvious consequence of assuming a uniform distribution over fitness functions, which is the assumption in the NFL Theorem. Your entire post in fact argues against this NFL assumption, yet you seem to still argue the relevance of NFL.perlopp_{January 3, 2008
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PaV(135), 1. Do you believe in premise (a), that fitness functions are best described as having a uniform distribution? After all, that is the assumption in the NFL Theorem. 2. The malaria paraiste has not done blind search. Blind search means that a new sequence is chosen randomly, thus, an offspring would have a genome that is completely unrelated to the parent.perlopp_{January 3, 2008
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It is so frustrating for me to read an article like this and see that people are actually enlightened by the authors obvious points. The computer simulations are lest we forget "computer simulations"- nothing less nothing more. Now it was always laughable to me that that people tried to use computers to justify one of the most complex processes known. We don’t even know all that much about the genetic code as it currently stands so why then do so many people claim to be sold on the theory of evolution via NS/RV based on a simple computer simulation? It is the same EXACT principal at work in the Global Warming hysteria crowed. This is a principal that I call "The Wanna Believe Principal." People wanna believe that global warming is happening and they wanna believe that everything evolved universal common ancestry via the Darwinian pathway so what do they do? - The go out and prove it. The only problem is that problems of this magnitude are not easily provable. Massive amounts of variable and historical data must be explained and taken into account if and when we are to program a simulation of long history. But even if all of the mathematicians and philosophers get together and are convinced that they have a good enough set of data and a god enough way to arrange that data "systematically" to prove their already preconceived bias - the question arises by what means can the natural history of the world be transferable to a computer simulation? The main reason that computers are not a transferable means f analogy from real history to simulation is that computers are logical devices. Computers are "communicable" and therefore have the ability to built into them to channel or facilitate the change necessary to get complexity and variation. They are based on the limbic system of the brain or the universal language of mathematics. Computers run on a system of 1s an 0s. Anyone can ad 1+1-1+2 and get 3. 1 to 3- novel SC! Hurray! But unfortunately as Gödel taught us mathematics is not a true description, let alone an explanation for the objective universe- it is incapable of proving itself. Chance is not like a computer. To put this more logically - change can be "artificially simulated" by a computer but "chance cannot artificially simulated a computer." And not only that but chance cannot simulate a computer! Which is what is required to explain the origin of the experiment to begin with. Therefore it is fair to assume that the experiment is very helpful to the ID movement in that it shows that the natural unguided chance based universe of Darwin is incompatible with the Designed universe of theology and science fiction. It takes a very clever designer to design chance and even a more clever one make it do anything. Now I have said before that NFL is the best book that I have ever read- and it was a bit of chance ironically that lead me to reading it in the first place as I ordered it from barns and noble without looking into the book at all of the advanced logic and mathematics involved, nonetheless, I plowed through it and was absolutely amazed. NFL is to me THE heart of the ID movement and its theoretical research project. As it has been said- that nothing makes sense outside of the theory of evolution - I would like to change that statement slightly to “Nothing makes sense outside of the theorems of NFL.” Dembski, Mad Props to you!Frost122585_{January 3, 2008
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perlopp (130); "Now, you seem to claim that NFLT does apply in biology, yet you talk about “clustering” which sounds like you do not believe premise (a). I’m trying to understand your point but it’s not easy." Haggstrom's premise is that if one or two nucleotides of a genome change, then the fitness for that genome falls to zero. If the fitness falls to zero with such a small amount of change, then, given the known mutation rate for genomes, nothing should exist. Ergo, NFL theorems cannot apply to the biological realm. Here's where he is hugely wrong. Most of the coding portions of the genome readily accept change without loss of fitness. We call that neutral substitution, or neutral mutations. If a protein is coded by a sequence 1,000 bases long, then 600 of them could become whatever it wants and life goes on. Does this prove Haggstrom to be correct? No. In post #55, I do two things. First I point out that we already have an example, courtesy of Behe, which as gone through more cycles of reproduction over the last 50-60 years than all of mammalian species have gone through since they began 65 million years ago; i.e., the malarial parasite. Ergo, its genome has gone through a 'blind search' of epic proportions. The whole while it has been in a titanic struggle with chloroquine. It has built up a resistance. How has it done so? Did it eliminate a gene? Did it manufacture a gene? In this tremendous 'blind search' for a solution to chloroquine, what did it come up with? The answer: two a.a. substitutions. Second, I do the math, and show that, as a rough calculation, the two substitutions represent a fitness function of around 1 in 10^150. When you put this all together, this means that the genome is capable of two things: (1) it is capable of 'clustering' to a great degree around 'neutral sites' of the genome, AND, (2) it has fitness functions for certain parts of the genome that fall off at almost an infinite angle. What does this mean? It means that the genome can endure 'neutral' mutations quite easily, but that it cannot endure mutations in more critical parts of the genome. Thus the genome CAN endure known mutation rates while also fulfilling the conditions that NFLT , per Haggstrom, require. And, we have evidence of that in the case of P. falciparum, the malarial parasite.PaV_{January 3, 2008
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kairos(133), The NFLT says that the probability of any particular sample is the same regardless of algorithm. In your example, compare blind search to adjacent-point search with the first point chosen randomly in each case. Now consider a sample of two consecutive high fitness values ("out of the flat landsacpe"). With blind search you must find such a value twice. By independence, the probability is p^2 for some very small p. With adjacent-point search, you need to find it once which has probability p but the conditional probability in the next step is much higher than p; thus beating blind search.perlopp_{January 3, 2008
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#129 perlopp
You don’t have NFL in your example as searching adjacent points beats blind search.
No, this isn't the case. To have a whichever advantage in searching adjacent points it is necessary that at least one of the points involved in the search are out of the flat landscape. But the probability that this does really occur is put to 0 by the condition |S|^|V|>>v*w; in fact it's a >> involving thousands and more magnitude orders between the cardinalities of the two sets.kairos_{January 3, 2008
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kairos(130), But your eaxmple does not work. Besides, Semitoic gave a reference to necessary and sufficient conditions for NFL earlier.perlopp_{January 3, 2008
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PaV(126), Let me try again; here's the bare bones of Haggstrom's argument: Dembski says that we only have two choices: (a) uniform distribution, which is when NFLT applies(b) design Haggstrom argues against this dichotomy by pointing out that the uniform distribution is unreasonable and that there is nothing mysterious about it. Doesn't take much biology to make that point I think. Now, you seem to claim that NFLT does apply in biology, yet you talk about "clustering" which sounds like you do not believe premise (a). I'm trying to understand your point but it's not easy.perlopp_{January 3, 2008
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#127 PaV
Isn’t your argument basically a mathematical version of Dembski’s “displacement problem” in that to find the target–the fittest location, you have to know which “f” to use; i.e., f belonging to M?
That is the abvious consequence. But IMHO what's rally important is that NFLT isn't constrained to uniform distribution but it's appliable in a wider way, so that Haggstroem's criticism falls just before to start. Moreover consider that the subset M I have defined is directly appliable to all the typical situations in Biology. So, all the anti NFLT Haggstrom's arguments based on genome clusters would be anyway not significant.kairos_{January 3, 2008
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kairos(125), You don't have NFL in your example as searching adjacent points beats blind search.perlopp_{January 3, 2008
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semiotic Does anyone here find it obvious that both statements are true? I find it obvious that both could be true but not obvious that they both are indeed true - they could be wrong but they are not contradictory. One is an unflattering critique of Dembski's application of NFL to biology and the other is a general position statement on NFL and biology. It appears Wolpert thinks Dembski didn't do a good job applying NFL to biology (the main objection is lack of quantification and precision hence "jello") but that doesn't mean Wolpert rejects NFL as applicable in biology. Indeed Wolpert holds it is quite applicable to biology. In more of an aside he says there are free lunches in coevolution but that no (or at least too few) coevolutionary situations arise in biology to make coevolution and NFL relevant to it and then reiterates that the original (not coevolutionary) NFL theories are indeed relevant in biology. What don't you understand?DaveScot_{January 3, 2008
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kairos #125 Isn't your argument basically a mathematical version of Dembski's "displacement problem" in that to find the target--the fittest location, you have to know which "f" to use; i.e., f belonging to M?PaV_{January 3, 2008
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perlopp #119 I understand his argument in exactly the same way. But I think he's wrong. In my post, #55, I lay out the argument for why he's wrong. I hope you've read it. How about a little history here. When gel electrophoresis first came onto the scene, mainly the 60's I believe, it afforded the first chance for scientists to extract proteins rather easily. So scientists began comparing proteins from differing individual organisms. The sequence of a.a.s was then a glimpse of the corresponding sections of DNA. What did scientists expect? They expected homogeneity. Why did they expect homogeneity? Because Darwinian theory, viz., selection, dictated that across a species the DNA should remain the same or the creature would die. Well, it turned out that proteins from organisms from the same species varied considerably at many a.a. locations. It was because of this 'surprise' discovery that the Neutral Theory of evolution developed, effectively dropping the whole notion of selection. Bottom line, don't use Darwinism to argue for or against anything scientific. Because of neutral mutations, fitness functions have to incorporate the reality that the majority of nucleotides along the stretches of coding DNA can change into whatever they like. What does this generate in 'fitness space'-------clustering. As I say, Haggstrom's math looks fine. But he shouldn't argue against the use of NFLT in evolution based on bad biology.PaV_{January 3, 2008
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#99 perlopp Sorry, message 122 wasn't complete because of a "less than" sign. I repost it.
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
Please consider the following case, in which the fittness function f:V->S is chosen according to a heavily non-uniform distribution. Let us consider the subset M of all the f's having the following characteristics: a) for almost all the |S|^|V| points we have that f(x) is very low or 0; b) there are only a maximum of v clusters (adjacent or linked points) in the solution space in which f(x)>>0, where each cluster is constituted by a max. of w neighbor points, and |S|^|V|>>v*w (in a 2-D solution space this means to have a huge flat fittness landscape with only few high and sharp pinnacles). Now let us suppose that f is not chosen according to a uniform distribution among |S|^|V| possibilities, but it is chosen (in a whichever way, uniform or non uniform) only among the set of f's belonging to M. This means that only f's belonging to M will be chosen while all the other f's have P(f)=0; a very non-uniform distribution. But in this case it is apparent that NFLT still hold. Q.E.Dkairos_{January 3, 2008
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#100
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:
Other people have already answered about. I like particularly the answer by Dave. :-)
The original NFL theorems assume uniform distributions on functions. ... functions is zero, contradicting the assumption of a uniform distribution.
It's here your mistake.kairos_{January 3, 2008
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#99 perlopp
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
Please consider the following case, in which the fittness function f:V->S is chosen according to a heavily non-uniform distribution. Let us consider the subset M of all the f's having the following characteristics: a) for almost all the |S|^|V| points we have that f(x) is very low or 0; b) there are only a maximum of v clusters (adjacent or linked points) in the solution space in which f(x)>>0, where each cluster is constituted by a max. of w neighbor points, and v*wkairos_{January 3, 2008
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Semiotic 007: What do you make of Meester's final irony: -----“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.” That statement seems reasonable to me. Apparently, you disagree with it. Could you explain why? Can you tie in what you are saying to the big picture.StephenB_{January 3, 2008
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