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

All, It was said earlier:
This leads to another reason why Dembski (2002) should not have indicated that the NFL theorems of Wolpert and Macready (1997) apply to biological evolution.
Now, the more I have thought about this and read both the primary literature and the Dembski/Marks publications, the more I think that the above misrepresents their point. Correct me if I'm wrong. Everyone is aware that there are a given set of search problems within genome space, which is a subset of all possible search problems; there are also many "target" regions which specify functionality islands in this space and there are biologically relevant fitness functions, which again, is a subset of all possible fitness functions. Now, I don't think Dembski, Marks or anyone else is arguing that all possible fitness functions are instantiated or even that it has conclusively been shown that the match of random-walk evolutionary search to the subset of biological search problems results in performance on the same level of efficiency as random blind search; to argue such I think is misleading or dishonest. From my reading of Demsbki, he is NOT saying that over the biologically *relevant* search problems and fitness functions an NFL situation occurs in which we should expect Darwinistic search to perform as random blind search would. He is, however, saying that NFL applies to the general problem of finding the right search algorithm for your particular search problem. The more correct information you have about the problem at hand, the better you are able to find a suitable algorithm that outperforms random blind search. So if biological search does indeed outperform random blind search on average over the various fitness landscapes then we can ask what are the chances we found this match of algorithm to search space structure by chance? The answer is quantifiable and this is the direction the "Active Information" framework approaches the question from.Atom_{January 6, 2008
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PaV (204):
Please tell me where it says anything about sets in NFL theorem
The domain of all functions in Wolpert and Macready (1997) is finite set X (in script), and the codomain is finite set Y (also in script). The set of all functions from X to Y is Y^X, and |Y^X| = |Y|^|X|. That is, the set of all functions from X to Y is finite, and a probability distribution over that set is discrete, not continuous. You have pointed us to an irrelevant Wikipedia article. While we're on the matter of discrete versus continuous, let's note also that functions with domain X are discrete, and thus your repeated invocation of the continuous Dirac delta function is inappropriate. You might want to read about the Kronecker delta.Semiotic 007_{January 6, 2008
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perlopp #196: I disagree with your second paragraph. I’m no follower of Dembski but here I have to defend him: He never states that any event with probability less than 10^-150 is impossible; only those that also satisfies some kind of “specification.” The Gettysburg Address has 272 words. At four letters/word, that is 1088 letters. The probability of this coming about by chance is 1 in 28^1088; this is well below that of the UPB of 10^-150. But, I assure you, it exists. What is “impossible” is not that the Gettysburg Address exists, but that it came about simply by chance. But you see, what’s impossible for blind chance, is easily possible for intelligent agents. BTW, since intelligent agency is involved, yes, indeed, the Gettysburg Address is a “specification”.PaV_{January 6, 2008
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semiotic 007 #195: To argue now that Dr. Dembksi would have been right if he had said something he did not is… odd. Did Haggstrom claim in 2002 that NFLT don't apply to biology, and did Dembski respond to this argument in 2002 when writing NFL? Of course not. Isn't it odd to expect Dembski to have addressed an arugment before it was ever made? We're simply arguing here for what is rather obvious from an intuitive standpoint. This isn't an argument that Dembski couldn't make himself, it's simply an argument he wouldn't bother taking the time to make, unless for some reason he needed to.PaV_{January 6, 2008
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#194 Semiotic 007 If you obtain your “real” distribution P by thresholding the given p (setting small probabilities to zero) and normalizing (i.e., to make the sum of probabilities over all functions equal to 1), then P diverges even further from the “nearest” distribution for which there is NFL than p does. It's not so for the basic condition Sum p=1 and the thresholding to 0 are two separate and non-overlapping operations. a) The first operation involves the rough probabilities associated to each x belonging to the solution space; here we can suitably use the theoretical p's associated to each x of any given fittness function f, where x belongs to V. b) The second operation involves the use of the p's to suitably compare the search possibilities of different algorithms, in particular random vs hillclimbing ones. Here and only here it's necessary to correctly characterize what happens in the real world. And in the real world in a solution space of cardinality, say, 10^1000,000 the probability to "hit" a subset with cardinality, say, 10^100 can be put 0 because UPB=10^-150>>10^-999,900. Put (too) simply, to get NFL, you have to make the small probabilities bigger and the big probabilities smaller. You have suggested just the opposite. Figure 4 in the English (2004) paper might make this more intuitive. NO, I haven't suggested so. This leads to another reason why Dembski (2002) should not have indicated that the NFL theorems of Wolpert and Macready (1997) apply to biological evolution. For any realistic model, there are more than 10^150 functions from genomes to fitness values, and thus p(f) is less than 10^-150 (the universal probability bound Dembski used in 2002) for all fitness functions f. That is, all fitness functions are effectively impossible when you posit a uniform distribution and apply the universal probability bound. Perlapp has already explained the difference, difference that is also present in my argumentkairos_{January 6, 2008
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PaV (201):
The NFLT says that no algorithm will do any better than a blind search.
Neither of Theorems 1 and 2 of Wolpert and Macready (1997) says that. The theorems imply that every algorithm has average performance over all functions (equally weighted) identical to that of random search. That all algorithms perform identically on particular constant functions is no more a contradiction than that some algorithms perform differently on non-constant functions. Random search is the average search, as Wolpert and Macready (1997) point out, and this is how Marks and Dembski treat it in their analytic framework. In fact, random search is equivalent to randomly (uniformly) selecting a deterministic search algorithm and then applying it. Thus for a typical fixed function, about half of all deterministic algorithms "do better" than random search is expected to do, and about half do worse. This is why, if you arbitrarily select an algorithm to apply to a given function, the active information is generally as likely to be negative as positive. It seems to me that some IDists have heard so long that random search is inefficacious that they are having a hard time grasping that it is average. To put things more simply, if you design a search algorithm to solve a problem you misunderstand, then random search will likely outperform your designed algorithm. Furthermore, almost all problems (functions, actually) are disorderly in the extreme, and thus are in no ordinary sense understandable. The probability of uniformly drawing a function for which design is meaningful is very small. That is, the choice of search algorithm is almost always arbitrary. A single execution of random search is equivalent to an arbitrary choice of algorithm. Furthermore, random search is almost always efficacious -- when the function is algorithmically random, almost all search algorithms are efficacious.Semiotic 007_{January 6, 2008
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perlopp #192: PaV: "A uniform distribution is an equal probability distribution over an interval." perlopp: That is one special case. You then suggest to me that I follow DaveScot's advise to "read more, and to write less." Two things: (1) some of your posts don't show up immediately, so when I respond there is literally nothing to 'read'; (2) Here's a link to what Wikipedia has to say about a uniform distribtuion. It's a 'definition', in fact. Please tell me where it says anything about sets in NFL theorem: http://en.wikipedia.org/wiki/Uniform_distribution_(continuous)#Standard_uniformPaV_{January 6, 2008
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#193 kairosfocus [Onlookers, Kairos and Kairosfocus are two very different persons. I am a J’can by birth and ancestry whose family has lived in several Caribbean territories, a physicist in my education base, an educator and strategic- management- in- the- context - of sustainability- of- development- in- a world- of- accelerating- and- transformational- change thinker in my work and service activities, and an Evangelical Christian [cf. this invited public lecture] living out here in Montserrat, where my wife hails from. Hi kairosfocus. I instead am European, a place where the dispute on ID has become a little warmer since two years but it's very far from being a hot argument. Instead my interest on the argument of telelogy in the world is quite old and it's enforced by my specific expertise in electronics and computer science. I have come to use kairos as a key concept in light of its appearance in Paul’s Mars Hill address, circa 50 AD in Athens, as recorded in Acts 17:24 - 27. K, what about you?] In my case I was inspired by 2 Chor 6,2: "legei gar KAIRW dektw ephkousa sou kai en hmera swthrias ebohqhsa soi idou nun KAIROS euprosdektoV idou nun hmera swthriaV"kairos_{January 6, 2008
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PaV (201):
The uniform distribution that is the premise of NFLT means that we consider all these functions to be equally likely. I disagree with this statement. The uniform distribution means that the “weighting” of each of the N elements is the same.
But you've just agreed, using terminology you find more intuitive. Probability distribution functions on discrete sample spaces are sometimes referred to as probability mass functions (in distinction to probability density functions on continuous sample spaces). The total mass of 1 is apportioned to (distributed among) the elements of the sample space. When the mass is distributed uniformly over the sample space, all elements have equal "weighting," which is to say that all elements are "equally likely."Semiotic 007_{January 6, 2008
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PaV(201), (1) you use N as the number of sequences. Why didn’t you use |S|^|V|? Because that is not the number of sequences. N denotes the number of sequences. You can also use the cardinality notation |V|, I just thought N looked nicer. At any rate, this is the number of elements in the domain V. The number |S|^|V| you mention is the number of functions from V to S. In my example, |S|=2, |V|=N, |S|^|N|=2^N. Each of the genomes has probability 1/|S|^|V| Same consistent misunderstanding. It's not a probability distribution over the genome space that is relevant to NFLT but a probability distribution over the space of functions from the genome space to the fitness space. PaV, I'd like to end our discussion here as this is getting quite pointless.perlopp_{January 6, 2008
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perlopp #183: I’ll try to explain how it works. There is a domain V consisting of all possible DNA sequences, thus V is what you call the genome space. A fitness function is a function from V to some other space S, f:V–>S. As Semiotic has pointed out, “fitness” is a hypothetical construct but we can undestand intuitively what it means. To make it easy, let us take S={0,1} (only two points) where 0 means low fitness, not likely to survive and 1 means high fitness, likely to survive. A fitness function now maps each sequence in V to a point in S. If the number of sequences is N, there are 2^N different such functions. Two points here: (1) you use N as the number of sequences. Why didn’t you use |S|^|V|? Because then you would have ended up with |S|^|S|^|V which involves the same symbol for two sets with completely different cardinalities|; which makes my point about Haggstrom’s confusion exactly. (2) To say that 2^N functions are involved is a confusing way of stating what I see as happening. What I see is this: you have ONE function, f, and this function f maps every one of the N elements of V onto S. And I don’t see 2^N elements in S, but N. After all, we’re talking about a function that is able to assess (hypothetically) the fitness of a given genomic combination. It’s going to be either 0 or 1, giving a sum of N 0’s and 1’s; how can you come up with both values for the same genome using the same function? Here’s the problem as I see it: When you say, “If the number of sequences is N, there are 2^N different such functions”, this is way off the mark. What you mean is that there are 2^N possible results: i.e., phase space of S has 2^N different possible configurations with each of 2^N functions giving a different result. This, it seems to me, is the more sensible, less confusing, way of speaking about it. The uniform distribution that is the premise of NFLT means that we consider all these functions to be equally likely. I disagree with this statement. The uniform distribution means that the “weighting” of each of the N elements is the same. For example, there is one function that maps all sequences to the point 1. This function says that all sequences have high fitness. I think we can agree that this is not a reasonable choice of fitness function but the premise in NFLT says that we consider it just as likely as any other function. Doesn’t this serve to identify that there is a problem with what you’re presenting? What do I mean? The NFLT says that no algorithm will do any better than a blind search. If all the elements of S are 1, the search would be over immediately; or, to put it another way: what would you be searching for if they’re all 1’s? In fact, your entire discussion implies that you consider fitness functions of a certain “diraquesque” type are much more likely than others. No, that’s not what I’m arguing. Each of the |S|^|V| elements have probability of 1/|S|^|V|. What I argue is that if you “cluster” a trillion of these probabilities, the probability (or improbability) of finding the cluster is hardly different at all from finding a single element. Instead of the probability of any element, that is, 1/ 10^3,000,000,000, the probability of the “cluster” would be 10^12/10^3,000,000,000, or 1/10^250,000,000. Both these improbabilities are Vast. The NFLT, or to put it another way, the ability to find these “clusters” using an algorithm that works better than a blind search, remains essentially unaffected by “clustering”. So you have two things at once: NFLT applying, and a “clustered” genome space that permits all kinds of mutations without an extreme loss of function. Thus, you are arguing for a very nonuniform distribution over the set of fitness functions (the set S^V) and the premise in NFLT is not satisfied. I think I’ve already answered this in an implicit way. Explicitly, we already know from nature the genomes that have fitness. We take these 100 trillion genomes, along with one trillion permutations of this genome that are known to be fit because of the neutral theory, and we do an infinite search, using infinite resources (because, after all, we’re playing God) to locate each and every one of them in S^V. Each of these, roughly, 10^25, genomes are then sorted into a 100 trillion “clusters”, with each of the trillion permutations of the genome of a particular species being “clustered” with it. All the other genomes are meaningless, with fitness value of ‘zero’. So they’re completely interchangeable. So, we now ‘randomly’ “cluster” all the remaining genomes into “clusters” of one trillion. Each of the genomes has probability 1/|S|^|V|. So each of these “clusters” will now have an equiprobability of [1/ |S|^|V|] x 10^12 instead of the 1/|S|^|V|. In our case, that means (10^12) x 10^-3,000,000,000 or 10^-250,000,000. All equiprobable. It’s a uniform distribution in the domain of f. And NFLT tells us ANY algorithm, including the Darwinian algorithm A (reproduction-mutation-selection), has no better chance of finding ANY of these “clusters” than a blind search does. And, of course, no one but God has such resources.PaV_{January 6, 2008
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kairosfocus(197), Whence comes all your anger? I only tried to help you understand the premise of the NFLT. Thermo-dynamics may the impose uniform distribution on various configuration spaces but that is not relevant to NFLT. In NFLT, the uniform distribution is over a function space. I have alrady explained it so I will not repeat myself. I have no interest in debating for debate's sake, only tried to explain a point that most here seem to have misunderstood.perlopp_{January 6, 2008
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PS: Kairos, we gotta get together sometime! [Onlookers, Kairos and Kairosfocus are two very different persons. I am a J'can by birth and ancestry whose family has lived in several Caribbean territories, a physicist in my education base, an educator and strategic- management- in- the- context - of sustainability- of- development- in- a world- of- accelerating- and- transformational- change thinker in my work and service activities, and an Evangelical Christian [cf. this invited public lecture] living out here in Montserrat, where my wife hails from. I have come to use kairos as a key concept in light of its appearance in Paul's Mars Hill address, circa 50 AD in Athens, as recorded in Acts 17:24 - 27. K, what about you?]kairosfocus_{January 6, 2008
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H'mm: Having got off my head of steam, maybe we can go back to using Wiki as a hostile witness -- more on this below -- i.e. one testifying against his will and/or making inadvertent but telling admissions:
Some computational problems are solved by searching for good solutions in a space of candidate solutions. A description of how to repeatedly select candidate solutions for evaluation is called a search algorithm. On a particular problem, different search algorithms may obtain different results, but over all problems, they are indistinguishable. It follows that if an algorithm achieves superior results on some problems, it must pay with inferiority on other problems. In this sense there is no free lunch in search.[1] Usually search is interpreted as optimization, and this leads to the observation that there is no free lunch in optimization.[2] . . . . The "no free lunch" results indicate that matching algorithms to problems gives higher average performance than does applying a fixed algorithm to all . . . .
Now, let's think about the underlying in-principle issues, in plain English. [Math symbols can and should be read as sentences, a point I always insisted on with my students, that they write out the sentences with appropriate connectying words: in effect so they could be scanned to see if they make sense, starting with "the RHS of an = sign restates what is on the LHS . . ." i.e I strongly dissent from the mindless use of the commonplace balance scales model as I am going to look at dimensionality equivalence of quantities on LHS and RHS, etc.] Okay, in steps, indenting for clarity in showing my step-by-step overall structure of reasoning:
1 --> Prof Wiki: Some computational problems are solved by searching for good solutions in a space of candidate solutions. Check. We have a configuration space and we have a chance + necessity only family of algorithms that are searching away, with multiple instantiations that are in effect a populaiton of candidates for being the fittest to survive. 2 --> A description of how to repeatedly select candidate solutions for evaluation is called a search algorithm.. Check, i.e., e.g. competitiveness among random variants within the ecosystem that selects "the fittest on average." (In the prebiotic world, there are difficulties but it is generally presumed by OOL researchers that some sort of chemically driven, statistical RV + NS on chemical functionality but not involving actual life-system - style biological reproduction is at work.] 3 --> On a particular problem, different search algorithms may obtain different results, but over all problems, they are indistinguishable. It follows that if an algorithm achieves superior results on some problems, it must pay with inferiority on other problems. In other words, on average, search algors will work very well only on problems they happen to be tuned for so on average the search algors' performance will even out. 4 --> In this sense there is no free lunch in search.[1] Usually search is interpreted as optimization, and this leads to the observation that there is no free lunch in optimization.[2] In short, we cannot rely on any given algor to solve everything. One has to pick -- or in this case, shape -- horses for courses. [How to do that, in our observation, takes intelligence . . .] 5 --> The "no free lunch" results indicate that matching algorithms to problems gives higher average performance than does applying a fixed algorithm to all . . . . H'mm: such as the underlying algorithmic architecture of RV + NS in its various prebiotic and biotic forms? 6 --> Further to this, we know that we are dealing with organised complexity showing itself as FSCI, and that on good "exhaustion of probabilistic resources" reasons, AND observation, agency is the best explanation of successful systems that manifest FSCI. [I use this subset of CSI as it its the relevant one, cf. discussion here in my always linked, app 3.] 7 --> That is, we have excellent reason to infer that RV + NS is a peculiarly ill-matched strategy for solving the OOL and body-plan level biodiversity problems. 8 --> So we have very good reason to infer that if the OOL and body-plan level biodiversity problems were solved [as obviously they were!], they were solved by other algorithms, tracing to agent action. For, across causally relevant accounts, the main options are chance and/or necessity and/or agency. The Evo Mat contention is that agency reduces at OOL and body-plan biodiversity [let's abbreviate: BPLBD] levels; but this is now running head-on into the origin of FSCI hurdle. 9 --> That is, we are back at the design inference as the best, empirically anchored explanation of OOL and BPLBD. And in so doing we saw that key principles- of- statistical thermodynamics considerations are relevant . . .
But, Prof Wiki protests . . .
A false inference, common in folklore and prominent in arguments for intelligent design,[7] is that algorithms do not perform well unless they are customized to suit problems. To the contrary, every algorithm obtains good solutions rapidly for almost all problems.[8] Unfortunately, almost all problems are physically impossible,[5] and whether any algorithm is generally effective in the real world is unknown.
Talk about talking out of both sides of your mouth!
10 --> First, in your direct- observation- based- EXPERIENCE, prof Wiki, have you ever seen a physically implemented algorithm that did not originate in an agent and was not customised by him to achieve success,usually after a fair bit of troubleshooting and debugging? [Onlookers, observe the studious silence in the just above excerpt on this point . . ..] 11 --> every algorithm obtains good solutions rapidly for almost all problems.[8] Unfortunately, almost all problems are physically impossible . . . BUT WE'S IS BE DEALING WITH PROBLEMS THAT WERE PHYSICALLY SOLVED, YOUR HONOR, MR WIKI, SIR! (Silence, again . . .) 12 --> And, honourable Professor, Sir, we have good statistical thermodynamics reasons to infer that RV + NS-architecture algors, however many instantiations and variants were possible across the gamut of our observed universe, cannot reasonably solve the first problem in the cascade: OOL. 13 --> For, most honorable professor, sir, probabilistic resources are rapidly exhausted (as shown in above posts by PaV and myself just to name two; and as is of course notoriously Dr Dembski's longstanding contention). 14 --> whether any algorithm is generally effective in the real world is unknown So, is this not a grudging acknowledgement of a point disguised as a dismissal? Indeed, arguably it is worse: we have about 60 years of experience with algorithm-based digital computers. There are no known generally effective real-world algorithms. So, Prof Wiki is issuing an IOU here not backed up by cash in his account! 14 --> And does it not also imply that real-world considerations are relevant to the issue of the utility or otherwise of the algorithmic architecture -- the meta-algorithm if you will -- proposed as the king of all real-world problem solvers: RV + NS in one form or another?
Or, as Dembski and Marks put it in their Info Costs of NFL paper that responds to Haggstrom:
Abstract—The No Free Lunch Theorem (NFLT) is a great leveler of search algorithms, showing that on average no search outperforms any other. Yet in practice searches do outperform others. In consequence, some have questioned the significance of the No Free Lunch Theorem (NFLT) to the performance of search algorithms. To properly assess the significance of the NFLT for search, one must understand the precise sources of information that affect search performance. Our purpose in this paper is to elucidate the NFLT by introducing an elementary theoretical framework for identifying and measuring the information utilized in search. The theory we develop [GEM: so, they are EXTENDING and APPLYING the NFL framework . . . in light of elaborating key concepts in it] shows that the NFLT can be used to measure, in bits, the fundamental difficulty of search, known as “endogenous information.” This quantity in turn enables us to measure, in bits, the effects of prescribed implicit knowledge for assisting a search, known as “active information.” Such knowledge often concerns search space structure as well as proximity to and identity of target. Active information can be explicitly teleological or can result implicitly from knowledge of the search space structure. The evolutionary simulations Avida and ev are shown to contain large amounts of active information.
Professor Wiki, I want my money back for this course! (Oops, it's "free" -- guess I shouldn't expect to get the full straight dope easy for free . . . ? After all:
there's no free lunch!)
GEM of TKIkairosfocus_{January 6, 2008
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PL, re 193: Especially . . .
Your discussion about thermo-dynamics may be brilliant for all I know but it is nevertheless irrelevant for the NFLT . . .
First, in the real world, the vital issues are strongly linked to thermodynamics and thence -- from the statistical perspective -- to configuration spaces, populations of possible energy and mass distributions and thence relative statistical weights of related observable macrostates. So, until the issues on such are credibly and forthrightly addressed, most of the above thread is so much empty metaphysical speculation. In short, I have relegated the NFLT issues to in effect at most a footnote. For, whether or not Dr Dembski is right on his key NFLT contentions [and, FYI he is a competent Mathematician in his own right and published his claim in a peer-reviewed monograph, so the reasonable presumption is that he knows what he is talking about until and unless it can be cogently shown otherwise], the stat thermodynamics and its probabilistic resources challenge to the alleged spontaneous generation of biofunctional information is the 800 lb gorilla that is tapping you on the shoulder. For, the issue is not what is LOGICALLY (or even in the barest sense PHYSICALLY) possible -- which includes a tornado in a junkyard assembling a 747 by an incredibly lucky clustering of parts and forces -- but what is reasonable relative to the available probabilistic resources of the observed cosmos. Here is famed OOL researcher Robert Shapiro in Sci Am recently on how this sort of reasoning comes across to him, on the RNA world type hypothesis [though he evidently does not see how this also equally speaks to his own metabolism first OOL models!!!]:
The RNA nucleotides are familiar to chemists because of their abundance in life and their resulting commercial availability. In a form of molecular vitalism, some scientists have presumed that nature has an innate tendency to produce life's building blocks preferentially, rather than the hordes of other molecules that can also be derived from the rules of organic chemistry. This idea drew inspiration from . . . Stanley Miller. He applied a spark discharge to a mixture of simple gases that were then [GEM: not now!] thought to represent the atmosphere of the early Earth . . . . Two amino acids of the set of 20 used to construct proteins were formed in significant quantities, with others from that set present in small amounts . . . more than 80 different amino acids . . . have been identified as components of the Murchison meteorite, which fell in Australia in 1969 . . . By extrapolation of these results, some writers have presumed that all of life's building could be formed with ease in Miller-type experiments and were present in meteorites and other extraterrestrial bodies. This is not the case . . . . The analogy that comes to mind is that of a golfer, who having played a golf ball through an 18-hole course, then assumed that the ball could also play itself around the course in his absence. He had demonstrated the possibility of the event; it was only necessary to presume that some combination of natural forces (earthquakes, winds, tornadoes and floods, for example) could produce the same result, given enough time. No physical law need be broken for spontaneous RNA formation to happen, but the chances against it are so immense, that the suggestion implies that the non-living world had an innate desire to generate RNA. The majority of origin-of-life scientists who still support the RNA-first theory either accept this concept (implicitly, if not explicitly) or feel that the immensely unfavorable odds were simply overcome by good luck.
See my point? That's why I have raised this issue. And, that is PaV's underlying point, too; including on the Dirac Delta Function-like nature of even very generously large estimates of archipelagos of biofunctional states under evo mat assumed OOL conditions or body-plan level biodiversification by chance + necessity only conditions. Now, instead of addressing this material -- and always linked, BTW -- context, you went on to a further dismissal and to do that, made a -- IMHCO -- ludicrous, ill-founded judgement on my understanding of logic and its applicability to the real world. If you want to seriously evaluate my understanding of the logic of physically related mathematical considerations, the above linked on the thermodynamics issues is a good place to start. Thence you may wish to look here for more on the wider issues of reasoning and believing across worldviews options. Failing such, I make a fair comment: your arguments -- for sadly good reason -- would then come across as contempt-driven dismissive rhetoric typical of Darwinista debaters and their fellow travellers. Recall, kindly, that Dawkins is the one who has insistently championed the alleged quadrilemma that those who reject evo mat are ignorant or stupid or insane or wicked. (Fallen and fallible I freely acknowledge. But on this, to help turn down the voltage on this overheated cultural issue, kindly show me to be wrong on the merits of the wider issue before using rhetoric that, frankly, comes across as in effect dismissing me as too dumb to figure out mathematical logic and its relevance to the real world.) FYFI, I have designed and built systems that are based on the bridging of mathematical logic to the real world of information-bearing and using systems. So, much of my view on the utter implausibility of the Darwinista "lucky noise" thesis -- and now a "successful search algorithms by chance + necessity only" thesis -- stems from that experience. Not mere speculation or in- the- teeth- of- abundant- "facts" religious commitment; another convenient and commonly met with rationalist rhetorical barb. I repeat, in the context of our empirically anchored knowledge, only agents produce the organised complexity that manifests itself as FSCI, especially artificial languages/codes and complex algorithms that successfully use these codes to execute real-world functions. In effect Evo Mat thought boils down to saying that our observations are wrong and that the underlying statistical thermodynamics principles that tie to those observations are also wrong. Then, it too often dismisses the counter-challenge to SHOW that this is so, by begging the methodological -- and frankly metaphysical -- questions. That simply raises my suspicions that it is the evo mat thinkers who don't understand -- and/or refuse to face -- the real issues, spewing up whatever cloud of rhetorical ink that is convenient on any given topic that will aid in escaping. That is a consistent pattern here at UD, and elsewhere. So, until trhe real-world challenges above are cogently addressed, the above on NFLT comes across -- in the context of the wider cultural debate -- as at most making a mountain out of a molehill. At worst, it is Dawkins-style Village atheist rhetoric based on a one-sided presentation of an issue. So, kindy understand my comments above as calling for balance and context. (And pointing out how, IMHCO, on the evidence we have again seen grudging acknowledgement on the merits disguised amidst the rhetoric of dismissal and even contempt.) GEM of TKIkairosfocus_{January 6, 2008
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Semiotic(194), I disagree with your second paragraph. I'm no follower of Dembski but here I have to defend him: He never states that any event with probability less than 10^-150 is impossible; only those that also satisfies some kind of "specification." Obviously, if you choose uniformly from a set with more than 10^150 elements, you will get an outcome that has less than 10^-150 probability but you must get some outcome. If you shuffle two decks of cards with distinguishable backsides, there are more than 10^150 permutations but nobody, including Dembski, would argue that they are all impossible. I think the confusion in this thread is that too few of us understand that the uniform (or more general permutation invariant) distribution is over a certain function space and not the genome space. I've tried to explain it and so have you. Hopefully it helps somebody.perlopp_{January 5, 2008
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PaV, kairos, and others: I remind you that the criticism is of the argument Dr. Dembski made in 2002, which referred only to the NFL theorems Wolpert and Macready published in 1997. Other proven NFL results and your own ideas about NFL are irrelevant. Dembski's (2002) argument is Dembski's (2002) argument is Dembski's (2002) argument. To argue now that Dr. Dembksi would have been right if he had said something he did not is... odd.Semiotic 007_{January 5, 2008
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kairos (187):
But have you taken into account the uniformity that is produced by the real P lower bound (for example let’s take the value proposed by Dembski 10^-150)?
If you obtain your "real" distribution P by thresholding the given p (setting small probabilities to zero) and normalizing (i.e., to make the sum of probabilities over all functions equal to 1), then P diverges even further from the "nearest" distribution for which there is NFL than p does. Put (too) simply, to get NFL, you have to make the small probabilities bigger and the big probabilities smaller. You have suggested just the opposite. Figure 4 in the English (2004) paper might make this more intuitive. This leads to another reason why Dembski (2002) should not have indicated that the NFL theorems of Wolpert and Macready (1997) apply to biological evolution. For any realistic model, there are more than 10^150 functions from genomes to fitness values, and thus p(f) is less than 10^-150 (the universal probability bound Dembski used in 2002) for all fitness functions f. That is, all fitness functions are effectively impossible when you posit a uniform distribution and apply the universal probability bound.Semiotic 007_{January 5, 2008
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kairosfocus(191), PaV misunderstands & you agree with PaV => you misunderstand. Applied formal logic. Anyway, I recommend my post 183 that explains that the uniform distribution is over the function space and nothing else. The confusion among many here may stem from he fact that we are not using probabilities to describe something stochastic but rather to describe our degree of belief in the different functions (a so-called Bayesian perspective which may in itself be questioned in which case the entire discussion is pointless). Your discussion about thermo-dynamics may be brilliant for all I know but it is nevertheless irrelevant for the NFLT. As Semiotic has pointed out, the most general possible premise for NFLT is permutation invariance which essentially means that a very fit individual remains very fit after any rearrangement of its genome. If you believe that applies in biology, you can apply the NFLT; otherwise, not.perlopp_{January 5, 2008
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PaV(189), A uniform distribution is an equal probability distribution over an interval. That is one special case. However, in NFLT the uniform distribution is not over an interval but over a function space. You might want to consider DaveScot's previous advice to "read a little more and write a little less." I recommend posts 182 and 183.perlopp_{January 5, 2008
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Perlopp, 188: A] Re:
PaV has completely misunderstood the premises of the NFLT. As you agree with him, you may not have gotten it right either . . .
Neat dismissal- by - driveby- labelling attempt. Now, kindly deal with the real-world issue that starts from [a] getting to a plausible prebiotic soup thence to [b] the observed functionally specified complex information of life systems, and onward, [c] body-plan level biodiversity. [You will note that I studiously avoid abstract discussions of NFLT etc, cf. my always linked for a, b, c in reverse order.] In particular, to anchor all of the above to scientific issues:
1 --> the AVERAGE [i.e. typical/ reasonably expected] performance of unintelligently directed or structured "searches" across v. large configuration spaces. [These are the ones relevant to evolutionary materialist scenarios for OOL and body-plan level biodiversity.] 2 --> The required co-adaptation of config space and search algorithm to consistently out-perform the average, i.e the issue of active information/ functionally specified complex information as the condition of confining a search to the neighbourhood of archipelagos of success, and hill-climbing to optimisation etc. 3 --> Application of same to claimed prebiotic environments that credibly gets us to a feasible prebiotic soup, thence by chance + necessity only to the observed FSCI of life systems at cellular level without exhaustion of probabilistic resources of the cosmos, and without metaphysical artifices such as quasi-infinite arrays of sub-cosmi. 4 --> The commonplace observation that in all cases where we do directly know the causal story, FSCI as just outlined is the product of agency, e.g. the posts in this thread. [NB: these happen to be high-contingency digital data strings that are functionally specified and complex, where perturbation beyond rather narrow bounds gets to non-funcitonal nonsense as a rule.] 5 --> Now, put the same insights from above into analysing the likely effect of the attempted construction of algorithms and the associated design of codes by chance processes on the gamut of the observed cosmos. [In case you don't understand my point, cf my always linked, App 1 sect 6, here.]
Now on NFLT as a context of mathematical debates . . . B] NFLT and the origins of biologically relevant CSI: 1] PL, 183: The uniform distribution that is the premise of NFLT means that we consider all these functions to be equally likely. Actually, the context of this is best understood from say Harry Robertson's Statistical Thermophysics, as I cite in my always linked, from his analysis on the deep link between statistical thermodynamics and information theory concerns:
. . . It has long been recognized that the assignment of probabilities to a set represents information, and that some probability sets represent more information than others . . . if one of the probabilities say p2 is unity and therefore the others are zero, then we know that the outcome of the experiment . . . will give [event] y2. Thus we have complete information . . . if we have no basis . . . for believing that event yi is more or less likely than any other [we] have the least possible information about the outcome of the experiment . . . . A remarkably simple and clear analysis by Shannon [1948] has provided us with a quantitative measure of the uncertainty, or missing pertinent information, inherent in a set of probabilities [NB: i.e. a probability should be seen as, in part, an index of ignorance] . . . . [deriving informational entropy . . . ] S({pi}) = - C [SUM over i] pi*ln pi . . . . [where [SUM over i] pi = 1, and we can define also parameters alpha and beta such that: (1) pi = e^-[alpha + beta*yi]; (2) exp [alpha] = [SUM over i](exp - beta*yi) = Z [Z being in effect the partition function across microstates, the "Holy Grail" of statistical thermodynamics]. . . .[pp.3 - 6] S, called the information entropy, . . . correspond[s] to the thermodynamic entropy, with C = k, the Boltzmann constant, and yi an energy level, usually ei, while [BETA] becomes 1/kT, with T the thermodynamic temperature . . . A thermodynamic system is characterized by a microscopic structure that is not observed in detail . . . We attempt to develop a theoretical description of the macroscopic properties in terms of its underlying microscopic properties, which are not precisely known. We attempt to assign probabilities to the various microscopic states . . . based on a few . . . macroscopic observations that can be related to averages of microscopic parameters. Evidently the problem that we attempt to solve in statistical thermophysics is exactly the one just treated in terms of information theory. It should not be surprising, then, that the uncertainty of information theory becomes a thermodynamic variable when used in proper context [p. 7] . . . . Jayne's [summary rebuttal to a typical objection] is ". . . The entropy of a thermodynamic system is a measure of the degree of ignorance of a person whose sole knowledge about its microstate consists of the values of the macroscopic quantities . . . which define its thermodynamic state. This is a perfectly 'objective' quantity . . . it is a function of [those variables] and does not depend on anybody's personality. There is no reason why it cannot be measured in the laboratory." . . . . [p. 36.] [Robertson, Statistical Thermophysics, Prentice Hall, 1993
--> Such considerations, of course, are highly relevant to the move from pre-biotic physics and chemistry to life-systems by chance and necessity only. --> They also underscore the relevance of the Laplace [etc] criterion that if one has no information to specify another distribution of probabilites of states, a uniform distribution is indicated. On this, we can see the great success of stat thermodynamics. --> When we do have reason to assign a different distribution -- i.e we have more information about the system, then we assign divergent probabilities. --> Indeed, on Cytochrome C as I cited in 184, Bradley does just that following Yockey et al. [And, PL, that is part of why I cited this case, in answering to Bob O'H.] 2] A Wiki FYI:
In computing, there are circumstances in which the outputs of all procedures solving a particular type of problem are statistically identical [GEM note -- i.e on avg no-body does better than anybody else -- no free lunch] . A colorful way of describing such a circumstance, introduced by David H. Wolpert and William G. Macready in connection with the problems of search[1] and optimization,[2] is to say that there is no free lunch. Cullen Schaffer had previously established that there is no free lunch in machine learning problems of a particular sort, but used different terminology.[3] To pursue the "no free lunch" metaphor, if procedures are restaurants [they prepare meals on order to pre-defined procedures, reliably, at competitive costs and charge to make a profit] and problems are menu items [i.e the problem to be solved by the procedure is as just specified] , then the restaurants have menus that are identical except in one regard — the association of prices with items is shuffled from one restaurant to the next [here there is an averaging process . . .] . For an omnivore who decides what to eat only after sitting at the table, the average cost of lunch does not depend on the choice of restaurant [i.e he can apply intelligence to pick a good meal at a good price in a specific situation] . But a vegan who goes to lunch regularly with a carnivore who seeks economy pays a high average cost for lunch [the vegan pays for both lunches in effect!] . To methodically reduce the average cost of lunch, one must use advance knowledge of a) what one will order and b) what the order will cost at various restaurants. That is, reduction of average computational cost (e.g., time) in problem-solving hinges on using prior information to match procedures to problems.[2][3] In formal terms, there is no free lunch when the probability distribution on problem instances is such that all problem solvers have identically distributed results. In the case of search, a problem instance is an objective function, and a result is a sequence of values obtained in evaluation of candidate solutions in the domain of the function. For typical interpretations of results, search is an optimization process. There is no free lunch in search if and only if the distribution on objective functions is invariant under permutation of the space of candidate solutions.[4][5]
Now, of course, Wiki is not exactly an ID-friendly source, so I cited it to show that the basic ideas are as WD did put them. [I am a great fan of getting the basics right then looking at the elaborations.] In the context of OOL, Evo Mat advocates need to get to life on the gamut of the observed cosmos by chance + necessity only, without running into the sort of maximal improbabilities WD pointed to and which PaV admirably sums up. Then, they need to get to the body-plan level biodiversity and required increments of 100's of millions to thousands of millions of DNA base pairs, without similarly exhausting probabilistic resources. That requires in effect finding a short-cut: [a] life is written into the underlying chemistry of pre-biotic environments and [b] RV + NS mechanisms for creating body-plan level functional bio-information without agency exist. Just to start with on these, kindly let us know PL, where the empirical evidence for inferring to such based on observations exists. 3] Dirac Deltas . . . PaV, actually, they had to rewrite the definition of a function to accommodate the Dirac Delta! (It was too useful to be dismissed.) PL, PaV is pointing out and underscoring that when we look at archipelagos of functionality on the grand scale of the config space, they are so finely located that they act as though they are weighted points. Random searches starting at arbitrary points are overwhelmingly likely to miss them. Agents, of course, use active intelligence to narrow down tot he neighbourhood of such islands and chains of islands, and so can access them with far greater likelihood of success. Thus, the routine ability of agents to get to FSCI such as the posts in this thread. GEM of TKIkairosfocus_{January 5, 2008
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j@185 (and all, as always): I resisted getting into a debate of an off-topic point. But you insisted, and I responded by linking to an on-topic paper that stood to be of interest to everyone reading the thread. Only ellipsis in your quote of my comment (#84, you might have mentioned) makes things seem otherwise. Here I've emphasized some text you omitted:
Here is an outstanding paper that not only ties “competition in a bounded arena” to neo-Darwinism, but also gets us (pretty please) on-topic: Notes on the Simulation of Evolution. 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.
I say now to everyone, explicitly, that the confluence of statistics, thermodynamics, optimization, learning, and biology in the paper is something very rare. As regards this thread, what is most important is that Atmar addresses simulation of evolution in the abstract. The downside is that the paper is 15 years old, and that it has an engineering slant in places.Semiotic 007_{January 5, 2008
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Just a little follow-up to my remark about the Dirac Delta function (and as a way of visualizing minute “fitness” landscapes): Properly speaking, the Delta function is not a function; it’s a convenience that allows scientists to sum the probabilities that come up in QM in such a way as to incorporate them into integrals. The essence of the idea is much like I’ve stated. A uniform distribution is an equal probability distribution over an interval. The area (integral) underneath the interval has to add up to 1. With the Dirac Delta function, however, one “integrates”, i.e., takes the “area,” not underneath an interval, but rather underneath a point. Putting it that way, you can see that, properly speaking, this, geometrically, can’t be done. But, nature begs to differ. (As with “spectral lines” and much of QM) So, to get a grasp of the Delta function picture yourself taking a ‘point’ and pulling it upwards towards positive infinity. “Stretching” the ‘point’ in this way causes the point to shrink its width in proportion to the length it’s being stretched to. The total area must still equal 1 however. So, remembering we’re dealing with a probability density at a single point, if, for example, the probability at that single point is 1/100, we, then, must “pull” this single point upward to 100 the value of 100. The area, as you can see, now equals one. ____________________________ Now, here’s the connection to “fitness” landscapes. I mentioned in an earlier post, that examining the characteristics of a certain protein in the sequence space of its functional unit, scientists found the fitness space of the protein to be something on the order of 10^-84, meaning that the protein could tolerate only 1 in 10^84 possible nucleotide exchanges, or permutations, in the critical area. Well, when this kind of “fitness landscape” is drawn, it is commonly shown as some kind of combined set of ‘hills’ that falls off into the plane out of which they arise. This picture you commonly see, is nothing but a fiction. It’s not meant to be a fiction; it’s just that it isn’t being thought through carefully enough. Let me show what I mean. Let’s say you have a 19” monitor you’re looking at this on. Imagine a upward directed curve starting out from the bottom left of your monitor, rising to a peak which is way above the center of the screen, but that then falls off towards the far right corner, leaving a gap at the top of the screen. (We don’t know how ‘high’ this curve rises, but we know it’s much more than our screen can handle.) When the “fitness space” of a protein is 10^-84, that would mean that if what you see on the screen represents this “fitness space”, then proportionately, you would be larger than the universe by huge orders of magnitude. Here’s my calculation for the diameter of the “visible” universe: {[15 x 10^9 years (age of universe)] x[ 365 days/yr x 24 hrs/ day x 60 min./hr x 60 sec/min x 300,000 meters/sec (the speed of light)] x 2 (radius to diameter conversion)=(2.838 x 10^23 meters } You’re two meters; the screen is a half meter. So, roughly speaking, you would have to be 8 x 10^61 times bigger than the “visible” universe to be able to see the function across the screen the way I described it. Conclusion: only God can see this fitness function in this fashion. To draw the fitness function for such a protein, that is, as “falling off” in a curve like way, is simply a fiction (or to play God). It’s a straight line, of thickness 1/10^84 of whatever scale you’re using (i.e., effectively invisible), ‘stretching out’ above whatever line you’ve drawn as a baseline by 10^84 times the scale you’re using (effectively infinite). You might as well say that it is a line of infinitely small breadth, and infinitely long length; the closest thing to it would be something along the lines of the “spectral lines” of atoms.PaV_{January 5, 2008
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kairosfocus(184), 5 –> PaV [175] has therefore put the evident bottomline very well Except that PaV has completely misunderstood the premises of the NFLT. As you agree with him, you may not have gotten it right either. See my post (183) for an explanation of the setup for NFLT. Semiotic(177) also addressed PaV's confusion.perlopp_{January 5, 2008
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#171 Semiotic Even if you buy the reasoning of Igel and Toussaint, their conclusion is not really the end of the story. Despite the all-or-nothing sound of “no free lunch,” NFL is a matter of degree. This is just my point. I. and. T proved an iff condition for NFLT under the non-uniform assumption and argued correctly that this condition should not be verified in the real world. But real world isn't only a matter of not having all the possible functions permutations. It's also matter of strict bounds on the probabilities of what can really happen in the world. A whichever event with P equal to, say, 10^-1,000 isn't in the real world statistically different from an event with P equal to, say, 10^-1,000,000, because no one will really occur and their real P will be 0. It's in this sense that also non-uniform distributions can imply NFLT in the real world. English emphasizes that most functions have exorbitant Kolmogorov complexity — an observation complementary to that of Igel and Toussaint. That's correct. If p(f) is the probability that a human will refer to function f, I can give a persuasive argument (not really a proof, because no one knows much about p) that the distribution p is not even approximately one for which there is NFL. The gist is that there are common f for which almost all f o j cannot arise in practice. But have you taken into account the uniformity that is produced by the real P lower bound (for example let's take the value proposed by Dembski 10^-150)? The situation is messier with fitness functions “in” biological evolution, because they are hypothetical constructs. That's true but, as correctly stated by PaV, The data provided by Behe in EoE give enough confidence on the fact that decent searches are out of the possibilities of RM+NS in biologykairos_{January 5, 2008
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#175 PaV iIf, as it seems, your explanation is quite similar to my example I agree on your claim.kairos_{January 5, 2008
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Semiotic 007 (166): "The thing I hoped Atmar would make clear is that we can put abstract evolutionary principles to test without simulating biological organisms. If memory serves, he indeed emphasizes the principles, as opposed to the implementation details." Are you confused? This directly contradicts your stated intention at (84). You provided a link to it to try to teach me what "competition in a bounded arena" means:
“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…
I then showed that the paper actually supports my statement that competition doesn't really exist in Darwinian theory, not your statement that competition "is essential to evolutionary theory." (Besides, I don't deny that important conclusions of principle can be drawn from abstract evolutionary simulations, so there would be no reason for you to try to make this clear to me. -- I simply know that entirely baseless conclusions are often drawn by Darwinists. E.g., Avida, etc.) Semiotic 007 (167): "A fitness function merely says how good individuals are. The function may be obtained by measurements of physical individuals, and it should be clear in such a case that the measurements are in no way determined by human purpose." It is clear that characteristics of (most) physical organisms aren't determined by human purpose, but it's an unfounded assumption that they aren't determined by any purpose whatsoever. Whether physical evolution is teleological or nonteleological is an unresolved and contentious issue. (Didn't you don't know that?!) Semiotic 007 (167): "I recently used two methods to randomly generate many highly compressible functions. Random search consistently outperformed simple enumeration of candidate solutions, and a (1+1)-EA [evolutionary algorithm] consistently outperformed random search." It's impossible to judge the importance of this statement without seeing a concrete example. Could you please provide an example of equivalent or similar work, so that we can determine for ourselves the extent of the teleology and nonteleology in your method? Have you audited your work using the Marks/Dembski metric of active information?j_{January 5, 2008
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All: Been busy elsewhere. I think the best answer to the dilemmas and issues in this thread is to pause, take a walk, then come back and think about the issues in light of basic common sense. Pardon a few semi-random thoughts, to stimulate such: 1 --> First, indeed it is always logically possible that we can have nicely structured phase spaces and/or algorithms that are tuned to them. Given the complexity of the phase spaces in question of this nice type and the functionally specified, complex -- AKA "active" -- information in the associated algorithms, what is the most reasonable explanation of such if we see it happening but don't know through direct observation the sources of the space and the algorithms? 2 --> We are in the end dealing with the real world. The one in which Kenyon's biochemical predestination thesis on protein sequences went down in flames when the actual typical patterns of proteins was examined. [AND, BTW, what would be most likely responsible for a world in which in effect the laws of chemistry had "life" written into them?] 3 --> On Bob O'H's [in 3]: the whole approach of calculating CSI of proteins is flawed too, because those probabilities can’t be calculated either. I observe that first, the information carrying capacity of 20-state chained digital elements is not a mystery to calculate: 20^N for an N-length chain (the underlying logic of this information capacity calculartion is obvious). And, Bradley in his recent remarks on Cytochrome C summarises that in fact there is some failure to take up the fuoll space, i.e the amino acid residues are not equiprobable in fact empirically, as the leters of English are not equiprobable:
Cytochrome c (protein) -- chain of 110 amino acids of 20 types If each amino acid has pi = .05, then average information “i” per amino acid is given by log2 (20) = 4.32 The total Shannon information is given by I = N * i = 110 * 4.32 = 475, with total number of unique sequences “W0” that are possible is W0 = 2^I = 2^475 = 10^143 Amino acids in cytochrome c are not equiprobable (pi ? 0.05) as assumed above. If one takes the actual probabilities of occurrence of the amino acids in cytochrome c, one may calculate the average information per residue (or link in our 110 link polymer chain) to be 4.139 using i = - ? pi log2 pi [TKI NB: which is related of course to the Boltzmann expression for S] Total Shannon information is given by I = N * i = 4.139 x 110 = 455. The total number of unique sequences “W0” that are possible for the set of amino acids in cytochrome c is given by W0 = 2^455 = 1.85 x 10^137 . . . . Some amino acid residues (sites along chain) allow several different amino acids to be used interchangeably in cytochrome-c without loss of function, reducing i from 4.19 to 2.82 and I (i x 110) from 475 to 310 (Yockey) M = 2^310 = 2.1 x 10^93 = W1 Wo / W1 = 1.85 x 10^137 / 2.1 x 10^93 = 8.8 x 10^44 Recalculating for a 39 amino acid racemic prebiotic soup [as Glycine is achiral] he then deduces (appar., following Yockey): W1 is calculated to be 4.26 x 10^62 Wo/W1 = 1.85 x 10^137 / 4.26 x 10^62 = 4.35 x 10^74 ICSI = log2 (4.35 x 10^74) = 248 bits He then compares results from two experimental studies: Two recent experimental studies on other proteins have found the same incredibly low probabilities for accidental formation of a functional protein that Yockey found 1 in 10^75 (Strait and Dewey, 1996) and 1 in 10^65 (Bowie, Reidhaar-Olson, Lim and Sauer, 1990).
4 --> That looks to me suspiciously like an a classic a priori probability based on observed patterns to me [incrementing from the well known Laplace [etc] principle of indifference [cf Robertson's use of it in developing informational approaches to statistical thermodynamics, e.g. app 1 my always linked], that one assigns uniform likelihood where there is no reason to infer to the contrary; of course one handicaps in light of such observations], i.e the key element in calculating information and informational entropy. [BTW, is anyone here prepared to argue that English text is most likely explained as chance + necessity on grounds that the distributions of the letters are non-uniform and that for instance there are key clusters of likelihood, i.e redundancy such as "qu" etc?] 5 --> PaV [175] has therefore put the evident bottomline very well:
If we mentally try to visualize what’s going on, we can look down on a sea of two-dimensional space. At each location, that is, each point[I would say cell -this is a discrete space!] , of this two-dimensional space we find a permutation of a 3,000,000,000 long genome. As we look down onto this 2D space, these 100 trillion “high fitness” genomes, along with each of their trillion “high fitness” permutations, are randomly dispersed on this plane. What we’re going to do is to “pull together” all of these trillion of “high fitness” permutations to form a cluster. (After all, they’re ‘independent’ of one another) We end up with 100 million clusters, consisting of one trillion permutations. We could have, admittedly, “clustered” all 10^25 (100 trillion x one trillion) together. But, if we were to do a blind search for just that one cluster, it would be much harder to find than having 100 trillion “clusters” (of a trillion permutations) throughout the space of all possible genomes. Now in this configuration of genome space we have “clustering”; in fact, we have it to a staggering degree: viz., one trillion viable permutations per genome. So, [per model just proposed] if the human genome were to experience a mutation anywhere along its length, the likelihood of it not being viable would be 1 in a trillion. So, again, we have the space of all possible genomes within which are to be found, randomly (again, giving the best possibility of being found by search), 100 trillion “clusters” of a trillion permutations. Once we’ve pulled all these permutations together and formed 100 trillion “clusters” of a trillion permutations each, then the space, G, of all possible genomes is smaller by roughly 10^25 genomes. But 10^25 represents 1/4,000,000,000 of G, leaving G essentially unaffected in size. Now, what we have left is a uniform distribution of size 10^1,000,000,000 among which are to be found generously realistic “clusters” of genomes for every living being imaginable. The odds of hitting the target, that is, any one of the 100 trillion “clusters” of genome permutations, through blind search is 10^25/10^1,000,000,000= 1 in 10^4,000,000. You can’t argue that the “clustering” I propose has in any significant way changed the uniform distribution of G, the space of all possible genomes. Nature must navigate this way using, per Haggstrom, Darwin’s algorithm A (reproduction-mutation-selection) to find its way through this uniform distribution. But since it is a uniform distribution, we know that it’s no better than ‘blind search’, and we know that G is to Vast for blind search to work. This is where the Explanatory Filter, that Dembski describes, would tell us that since randomness cannot explain the “discovery” of living genomes, then design is involved.
And, BTW, IMHO [NB, Mark, 12], that bottomline looks a lot like the point I made way back at the top of the thread. Sorry if ti is painful, but it does seem to me well-warranted, given the summary just given vs statements from the authors in question like Hagstom's:
“My debunking of some dishonest use of mathematics in the intelligent design movement
. If the sort of summarised estimates above are "dishonest," kindly show me why and how. GEM of TKIkairosfocus_{January 5, 2008
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PaV, I'll try to explain how it works. There is a domain V consisting of all possible DNA sequences, thus V is what you call the genome space. A fitness function is a function from V to some other space S, f:V-->S. As Semiotic has pointed out, "fitness" is a hypothetical construct but we can undestand intuitively what it means. To make it easy, let us take S={0,1} (only two points) where 0 means low fitness, not likely to survive and 1 means high fitness, likely to survive. A fitness function now maps each sequence in V to a point in S. If the number of sequences is N, there are 2^N different such functions. The uniform distribution that is the premise of NFLT means that we consider all these functions to be equally likely. For example, there is one function that maps all sequences to the point 1. This function says that all sequences have high fitness. I think we can agree that this is not a reasonable choice of fitness function but the premise in NFLT says that we consider it just as likely as any other function. In fact, your entire discussion implies that you consider fitness functions of a certain "diraquesque" type are much more likely than others. Thus, you are arguing for a very nonuniform distribution over the set of fitness functions (the set S^V) and the premise in NFLT is not satisfied. The more general premise of permutation invariance is not a rescue as it essentially implies that fitness is unaffected by any rearrangement of the genome.perlopp_{January 4, 2008
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PaV(179,180), Haggstrom consistently uses the notation V for the domain and S for the range of a function. The set of functions from V to S is denoted S^V and it is over this set the uniform distribution is assumed in the NGLT. You are constantly confusing different sets with each other and also the sets themselves with their cardinalities. Haggstrom's paper is actually very pedagogical if you take the time to read and understand (even if you disagee with his conclusions).perlopp_{January 4, 2008
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