Submitted by admin on Tue, 2006-08-29 21:46. Dembski, William A. | Specified Complexity

Contents

1. Preamble
2. Peer Review

3. Argument from Ignorance
4. Tornado in a Junkyard
5. Short Responses
       5.1 Uniform Probabilities
       5.2 The No Free Lunch Theorems
       5.3 Specification
       5.4 Algorithmic Information Theory

       5.5 Predictive Power of Darwinian Evolution
       5.6 Explanatory Power
       5.7 Wein's Acknowledgment
6. Conclusion

he Talkorigins Archive recently posted my critique of William Dembski's book No Free Lunch, entitled Not a Free Lunch But a Box of Chocolates, in which I thoroughly analyzed and refuted his arguments. Dembski quickly responded with an article entitled

Obsessively Criticized But Scarcely Refuted: A Response To Richard Wein. Although that article purports to be a response to my critique, it is in fact largely a recapitulation of arguments from No Free Lunch which ignores my refutations of them. In the few instances where Dembski has made a serious attempt to address my arguments, he almost invariably misconstrues them. Not one of my arguments has been satisfactorily addressed.

I invite any skeptical reader to cross-check my original critique with Dembski's response. To facilitate such a cross-check, this article uses the same section names and numbers as Dembski's and I provide links to the relevant sections of my critique.

All quotations labelled "Wein:" are from my critique and those labelled "Dembski:" are from his response, unless otherwise indicated.

1. Preamble

I begin, like Dembski, with some peripheral issues, before getting down to the technical issues in section 3 below.

Since he thinks it will work to his advantage here, Dembski makes some appeals to authority. He correctly points out that I have little authority, possessing only a humble bachelor's degree (in statistics). I am happy to let my arguments be judged on their merit, and would not ask anyone to accept them on my authority. Dembski should be wary of casting stones, however, since he himself criticizes experts in fields where he has no qualifications at all, such as biochemistry.

He also asks how the eminent endorsers of No Free Lunch can "think NFL is the best thing since sliced bread" if it is as bad as I argue it is. Perhaps he should ask himself how the far more eminent and numerous supporters of evolutionary theory can be so convinced by it if it is as bad as antievolutionists say. The antievolutionist is ill-placed to make appeals to authority when the overwhelming weight of scientific authority is against him.

Regrettably, advanced academic qualifications are no safeguard against falling into the trap of pseudoscience, especially when powerful dogmatic convictions are at stake.

2. Peer Review

For all the length of his discussion of peer review, Dembski fails to refute any of the facts that I presented (critique section 8). Most important, he is unable to name even one statistician or information theorist who approves of his work in their fields, confirming my suspicion that there are none.

While remaining completely silent on the subject of information theorists, Dembski attempts to explain the lack of support from statisticians by suggesting that his statistical claims are more appropriately judged by philosophers of science. I do not dispute that some philosophers have expertise in the field of statistics. But I note that he preferred to claim the support of statisticians when he thought he could get away with it:

Interestingly, my most severe critics have been philosophers (for instance Elliot Sober and Robin Collins...). Mathematicians and statisticians have been far more receptive to my codification of design inferences. [NFL, p. 372n2, and "Intelligent Design Coming Clean"]

Will he now retract his claim that statisticians have been receptive to his work?

In his article, Dembski claims that his method of calculating perturbation probabilities constitutes "a contribution to the applied probability literature." Has he submitted it to a journal of applied probability? Or is this yet another claimed contribution to a technical field that is best judged by philosophers?

3. Argument from Ignorance

Dembski begins this section by repeating the claim that his eliminative method of design inference is "inductively sound", based on the same absurd argument which I have already refuted (critique section 3.6). He makes no attempt to address my argument.

Next, he repeats his claim that it is possible to rule out unknown material mechanisms:

Dembski: Specified complexity can dispense with unknown material mechanisms provided there are independent reasons for thinking that explanations based on known material mechanisms will never be overturned by yet-to-be-identified unknown mechanisms.

In No Free Lunch an attempt to dispense with unknown material mechanisms was known as a "proscriptive generalization", but that term appears nowhere in Dembski's current article. It is unclear whether this is just a matter of inconsistency, or whether he now feels the term was an unwise one, suggesting a degree of certainty that he cannot justify. Since he has not acknowledged any change in his argument, I will continue to use his old term for the sake of consistency. I will also assume that his "material" mechanisms are synonymous with the "natural" mechanisms of No Free Lunch. Dembski's frequent unacknowledged changes of terminology do nothing to enhance the clarity of his arguments.

The proponent of an argument from ignorance always believes he has sufficient reasons for thinking that his explanation will not be overturned by a yet-to-be-identified unknown mechanism. So the fact that such reasons exist does not save the argument from being one of ignorance. It is an argument from ignorance because it is based not on evidence for the proposed explanation but on the purported absence of any other explanation.

In No Free Lunch, Dembski defined arguments from ignorance as being arguments of the form "not X therefore Y" (p. 111). But this is just the type of purely eliminative argument that he is making: not material, therefore design. Whether he eliminates material mechanisms by eliminating known mechanisms individually or by trying to rule out unknown mechanisms through proscriptive generalizations, this is still a purely eliminative argument.

Dembski continues by giving an example of a proscriptive generalization against alchemy. But the point is made needlessly, since I have already agreed with Dembski that proscriptive generalizations can be used to rule out some categories of possibilities (critique section 3.2). The point is irrelevant, since these are arguments against possibilities not arguments for a hypothesis. In terms of Dembski's "not X therefore Y", they are a "not X"; they are not a "therefore Y". Scientists did not argue "not alchemy, therefore modern chemistry".

Next, we have the example of a combination lock, which I did not discuss in my critique, so I'll consider in some detail here. Dembski argues as follows:

Dembski: The geometry and symmetry of the lock precludes that material mechanisms can distinguish one combination from another--one is as good as any other from the vantage of material mechanisms.

Not at all. There may be a flaw in the mechanism which causes it to favour some combinations over others. Or the lock may be flawed in some other way. No matter how carefully the lock has been inspected, we cannot completely rule out that possibility.

Consider an imaginary scenario in which a safe's combination dial is randomly rotated by natural forces. Let's say the safe is on a rowing boat at sea, and the rolling of the boat is sufficient to make the dial rotate. Now suppose that, while the sole occupant of the boat looks on, the safe springs open. For good measure, suppose that the rower is a locksmith who has thoroughly inspected the lock, found it to be flawless, closed the safe, and thoroughly randomized the dial, all since he has been alone on the boat. How will he explain the spontaneous opening of his safe? Let us say that he appreciates the sheer improbability of the safe opening by pure chance if it was operating to specification, and he rejects that explanation. Does he infer design? Or does he infer that, despite his thorough check, there was a flaw in the mechanism that caused it not to operate correctly? Even though it may seem implausible that the safe sprang open spontaneously, he will surely consider it even more implausible that someone boarded his boat and opened the safe while he was watching it, without him noticing, and he will prefer the former explanation. This is an "inference to the best explanation", or comparative inference. I discussed such inferences at some length (critique section 3.5). Dembski has completely ignored that discussion, and continues to insist that his eliminative inferences are the only option.

According to Dembski's logic, the rower should have inferred design, no matter how certain he was that no human agent could have been responsible, even if it required him to posit an unembodied designer. Dembski may respond that the hypothesis of a flawed mechanism is another relevant chance hypothesis which must be eliminated before inferring design. If he does so, he admits the fallacy of his argument that it is possible to "guarantee the security of the lock."

I should add that this discussion of proscriptive generalizations has no relevance to Dembski's argument for design in biology, since I have refuted his claim of a proscriptive generalization against Darwinian evolution of irreducibly complex systems (more on this below).

The remainder of Dembski's section is not a response to my critique at all, but is a long passage cut and pasted from one of his articles, with trivial changes. The article in question is the text of his recent talk at the American Museum of Natural History, which he has posted to the Internet under the title "Does Evolution Even Have a Mechanism?" Most of this is a rehash of arguments from No Free Lunch, and does not even belong in a section which purports to be addressing the "Argument From Ignorance" issue. I will address only the parts dealing with that issue.

Dembski: Isn't arguing for design on the basis of specified complexity therefore merely an argument from ignorance? Two comments to this objection: First, the great promise of Darwinian and other naturalistic accounts of evolution was precisely to show how known material mechanisms operating in known ways could produce all of biological complexity. So at the very least, specified complexity is showing that problems claimed to be solved by naturalistic means have not been solved.

Biologists have never claimed to know precisely how every biological structure evolved. So Dembski is attacking a straw man.

Dembski: Second, the argument from ignorance objection could in principle be raised for any design inference that employs specified complexity, including those where humans are implicated in constructing artifacts. An unknown material mechanism might explain the origin of the Mona Lisa in the Louvre, or the Louvre itself, or Stonehenge, or how two students wrote exactly the same essay. But no one is looking for such mechanisms. It would be madness even to try. Intelligent design caused these objects to exist, and we know that because of their specified complexity.

Once again, Dembski assumes that all our inferences of design use his eliminative approach. I have already addressed this claim (critique section 3.5). He has not responded.

I note that this section of Dembski's article contained not one direct response to any argument of mine. He made no attempt at all to refute my argument that his method of design inference is a purely eliminative argument, an argument from ignorance, and a god-of-the-gaps argument (critique section 3.3). He did not provide definitions of these terms and attempt to show that his method does not match them. He did not even attempt to challenge my definitions of these terms. Nor did he address my argument that the term "specified complexity" is an unnecessary middleman. Let me make that argument even simpler: why not replace

all relevant chance hypotheses eliminated --> specified complexity --> design

with

all relevant chance hypotheses eliminated --> design?

4. Tornado in a Junkyard

I pointed out (critique section 4.1) that Dembski's only probability calculation for a biological system is based on a hypothesis of purely random combination, or what I called a "tornado in a junkyard" scenario. Since such hypotheses are already universally rejected by biologists, I argued that the calculation was addressing a straw man hypothesis, and was therefore irrelevant. Dembski responds:

Dembski: Wein therefore does not dispute my calculation of appearance by random combination, but the relevance of that calculation to systems like the flagellum And why does he think it irrelevant? Because co-optation is supposed to be able to do it.

Dembski has not read my article carefully enough. I wrote:

Wein: No biologist proposes that the flagellum appeared by purely random combination of proteins--they believe it evolved by natural selection--and all would agree that the probability of appearance by random combination is so minuscule that this is unsatisfying as a scientific explanation. Therefore for Dembski to provide a probability calculation based on this absurd scenario is a waste of time. There is no need to consider whether Dembski's calculation is correct, because it is totally irrelevant to the issue.

There is nothing here about co-optation. I did not mention co-optation until the following section (where I called it "change of function"). So Dembski has entirely failed to address my argument. Nevertheless, I thank him for confirming that his calculation is based on a hypothesis of random combination.

At this point, let me interject a passage from Dembski's talk at the American Museum of Natural History, which he included in his section 3:

Dembski: Convinced that the Darwinian mechanism must be capable of doing such evolutionary design work, evolutionary biologists rarely ask whether such a sequence of successful baby-steps even exists; much less do they attempt to quantify the probabilities involved. I attempt that in chapter 5 of NFL (to which I'll return shortly). There I lay out techniques for assessing the probabilistic hurdles that the Darwinian mechanism faces in trying to account for complex biological structures like the bacterial flagellum. The probabilities I calculate--and I try to be conservative--are horrendous and render natural selection utterly implausible as a mechanism for generating the flagellum and structures like it.

There is no mention here that the probabilities were calculated under a hypothesis of random combination. On the contrary, there is a distinct implication that they were calculated under a hypothesis involving natural selection. We know this to be untrue, but listeners at the AMNH may have been misled by it. A reader unfamiliar with the tactics of antievolutionists might have thought that it did no harm to include an irrelevant calculation in No Free Lunch. But those of us familiar with antievolutionist rhetoric foresaw that it would be abused in the way we see here.

In my next section (critique section 4.2), I refuted Dembski's claim to have found a proscriptive generalization against the Darwinian evolution of irreducible complexity. Since this is an important point, I'll repeat the passage here:

Wein: Let us accept, for the sake of argument, that Dembski's definition is tight enough to ensure that IC systems cannot evolve by direct pathways. What has he said on the vital subject that Behe failed to address--the subject of indirect pathways? The answer is nothing. The crux of his argument is this:

Dembski [NFL]: To achieve an irreducibly complex system, the Darwinian mechanism has but two options. First, it can try to achieve the system in one fell swoop. But if an irreducibly complex system's core consists of numerous and diverse parts, that option is decisively precluded. The only other option for the Darwinian mechanism then is to try to achieve the system gradually by exploiting functional intermediates. But this option can only work so long as the system admits substantial simplifications. The second condition [that the irreducible core of the system is at the minimal level of complexity needed to perform its function] blocks this other option. Let me stress that there is no false dilemma here--it is not as though there are other options that I have conveniently ignored but that the Darwinian mechanism has at its disposal.[p. 287]

Wein: But there is indeed an option that Dembski has overlooked. The system could have evolved from a simpler system with a different function. In that case there could be functional intermediates after all. Dembski's mistake is to assume that the only possible functional intermediates are intermediates having the same function.

For once, Dembski appears to have read and understood my argument, but he makes no attempt to refute it. His proscriptive generalization is therefore dead. That leaves him with only appeals to ignorance and red herrings:

Dembski: For Wein to account for systems like the flagellum, functions of precursor systems must co-evolve. But that means the space of possible functions from which these co-evolving functions are drawn is completely unconstrained. This provides yet another recipe for insulating Darwinian theory from critique, for the space of all possible biological functions is vast and there is no way to establish the universal negative that no sequence of co-evolving functions could under co-optation have led to a given system.

Dembski is not required to establish a universal negative. He just needs to show that a design hypothesis is better, given the available evidence, than the hypothesis of purely natural evolution. But he rejects inferences to the best explanation, insisting on a purely eliminative mode of inference, and that puts him in the unenviable position of either establishing a "universal negative" or admitting there is a category of possibilities he has not eliminated. Since he cannot do the first and does not wish to do the second, he equivocates, first claiming that he has ruled out all Darwinian possibilities (his proscriptive generalization) and then, when it is shown he has not done so, complaining that the expectation was unreasonable. In short, he wants to have his lunch and eat it too!

Dembski: Let me suggest that there are further reasons to be deeply skeptical of Wein's co-optation scenario. First, specified complexity is used to nail down design in cases of circumstantial evidence, so if there should happen to be design in nature, specified complexity is how we would detect it. Thus, my probability calculation for the flagellum, in the absence of a counter-calculation by Wein, is prima facie evidence of biological design. This may not provide sufficient reason for convinced Darwinists to abandon their paradigm, but it gives evolution skeptics reason to consider other options, including design.

This is the crude argument from ignorance: having eliminated the absurd hypothesis of purely random assembly, we must infer design unless biologists can give an alternative hypothesis detailed enough to allow a probability calculation.

Dembski: Second, there is a whole field of study developed by Russian scientists and engineers known under the acronym TRIZ (Theory of Inventive Problem Solving) that details patterns of technological evolution...

Dembski argues that, because engineers do not use Darwinian methods to solve "inventive" problems, biological evolution cannot do so. The argument is an absurd non sequitur. Biological evolution can make billions of trials, thanks to large populations and unimaginable periods of time. Human engineers do not have such vast resources available. Furthermore, the premise of Dembski's argument is false. In recent years some engineering problems have indeed been solved using Darwinian methods, namely computerized evolutionary algorithms. Dembski himself gives an example: the "crooked wire genetic antennas" of Altshuler and Linden (NFL, p. 221).

Dembski: Third, and perhaps most telling, Wein needs fitness to vary continuously with the topology of configuration space. Small changes in configuration space need to correlate with small changes in biological function, at least some of the time. If functions are extremely isolated in the sense that small departures from a functional island in configuration space lead to complete nonfunctionality, then there is no way to evolve into or out of those islands of functionality by Darwinian means.

The notion of "functional islands" is misleading, as I will show below. But the essential point that Dembski seems to be making here is that there might not be a viable evolutionary pathway to the bacterial flagellum. This is just another appeal to ignorance. In his previous section, he made this appeal more explicit: "But what guarantee is there that a sequence of baby-steps connects any two points in configuration space?" Science is not in the business of giving guarantees, but of making inferences to the best explanation. (Note: "configuration space" is equivalent to the term "phase space" which Dembski used in No Free Lunch.)

Dembski: To clear away this obstacle to the Darwinian mechanism, Wein argues that the laws of nature guarantee the continuity that permits the Darwinian mechanism to flourish. According to Wein, smooth fitness landscapes are the norm because we live in a world with regular laws of nature and these are supposed to ensure smoothness.

Here, Dembski cites my argument from the regularity of the laws of nature, but that argument was only a response to Dembski's argument from the NFL theorems (see section 5.2 below). He is taking it out of context and treating it as a response to a different argument. He is also misreading it, since I wrote nothing about a guarantee.

Having failed to defend his argument from irreducible complexity, Dembski finishes this section by appealing to another argument. It is based on research that may be published in the next two years, and which allegedly will show that functional enzymes are located on isolated "islands of functionality" in configuration space. Since the research is not yet in and Dembski has not described the argument in any detail, it hardly deserves a response. Nevertheless, I will make a few comments:

• Dembski claims that this research will provide an opportunity for his method of "perturbation probabilities" to show its true merit. But his perturbation probabilities are based on a hypothesis of purely random combination of components, i.e. the "tornado in a junkyard" scenario. This scenario is just as irrelevant to the evolution of individual enzymes as it is to the evolution of the bacterial flagellum.

• He predicts that the research "will provide convincing evidence for specified complexity as a principled way to detect design and not merely as a cloak for ignorance." This is nonsense. The research cannot be used both to establish a result using Dembski's method and also as confirmation of the validity of that method. The conclusion that specified complexity is a cloak for the argument from ignorance follows from its definition, as I have already shown, and cannot be refuted by any amount of research.

• From the extremely brief description in No Free Lunch (p. 301), it appears that the configuration space in question is one in which the units of variation are individual amino acids. At best Dembski's argument might show that it is not possible to evolve from one island to another by multiple substitutions of individual amino acids. But biological mutation is not limited to such a process. Whole sequences of amino acids may be substituted by a single mutation (e.g. DNA shuffling). As with irreducible complexity, Dembski is attempting to shoehorn a complex biological process into an excessively simplistic model. He has overlooked a key element in that process.

  An interesting analogy may be noted with Dembski's example of attempting to evolve a computer program by means of random changes to its source code. While this cannot be achieved by changing single characters in a typical program, it can be achieved by changing larger elements of a program which is suitably structured. There is a field of study called "genetic programming" which is devoted to just this subject. For a brief introduction, see "Genetic Programming with C++".

5. Short Responses

5.1 Uniform Probabilities

One thing I was hoping to see in Dembski's response was a clarification regarding his two apparently different methods of determining specified complexity, the chance-elimination method and the uniform-probability method, as I have named them. At first he seems to deny the uniform-probability method, insisting that we must calculate probabilities with respect to all relevant probability distributions (i.e. chance hypotheses):

Dembski: As a criterion for detecting or inferring design, specified complexity must be assessed with respect to all the relevant probability distributions. Consequently, for complexity to obtain, the probability of the specified event in question must be less than the universal probability bound with respect to all the probability distributions (i.e., relevant chance hypotheses) being considered. (Note that this means the formula in the Law of Conservation of Information, I(A&B) = I(A) mod UCB, needs to obtain for every relevant probability distribution P, which gets converted to an information measure I by a logarithmic transformation.)

Unfortunately, the last part of this passage further obfuscates the nature of the Law of Conservation of Information (LCI). A scientific or mathematical law should tell us what does obtain, not what "needs to" obtain. It will help to sort out this confusion if I start by removing the disguise from the formula. The LCI's formula, "I(A&B) = I(A) mod UCB", is a disguised form of "P(R|H) ≥ α", the complement of the formula "P(R|H) < α" which is Dembski's criterion for rejecting a chance hypothesis (critique section 3.1). In other words, the LCI's formula states that the calculated probability is not small enough to reject the hypothesis. The disguise is implemented by means of the following transformations:

• Refer to the rejection region R as an "item of information" B, consisting of two parts T and E. The "target" T is just another name for the rejection region R. The outcome (or elementary event) E plays no part in the LCI, which only considers the probability of T, so can be ignored. In practice, B is just R in disguise. Thus, P(R|H) ≥ α becomes:

  P(B|H) ≥ α

• Leave out the chance hypothesis H (as this can be taken for granted):

  P(B) ≥ α

• Forget about computing a probability bound (α), and just use the universal probability bound (10^-150):

  P(B) ≥ 10^-150

• Make explicit some prior event or state A on which B depends:

  P(B|A) ≥ 10^-150

• Substitute the identity P(B|A) = P(A&B)/P(A) (see NFL, pp. 128-129):

  P(A&B)/P(A) ≥ 10^-150

  P(A&B) ≥ P(A) × 10^-150

• Transform probability into "information" by applying the function I = -log₂P:

  I(A&B) ≤ I(A) + 500

• Call 500 the Universal Complexity Bound (UCB) :

  I(A&B) ≤ I(A) + UCB

• This is the LCI as stated on p. 161. Now introduce Dembski's peculiar "mod" notation:

  I(A&B) = I(A) mod UCB

Remember that the LCI applies to events which "arose by natural causes" (NFL, p. 160). So, with the disguise removed, and taking Dembski's statement above at face value, this is what the LCI tells us: if an event arose by natural causes, then it needs to be the case that no relevant chance hypothesis gives rise to a probability small enough for that hypothesis to be rejected. But what is the purpose for which this "needs to" obtain? If Dembski means it needs to obtain or else we should infer design, then he is now saying we should infer design if even one relevant chance hypothesis can be rejected. However, his chance-elimination method tells us only to infer design if all relevant chance hypotheses can be rejected (NFL, p. 73). So this interpretation cannot be right.

Perhaps Dembski means that, if an event arose by natural causes, then it is the case that no relevant chance hypothesis gives rise to a probability small enough for that hypothesis to be rejected. But Dembski's "relevant" chance hypotheses are just those which we think (before we've calculated a probability) might be able to explain the observed event. Only one of them (at most) can be the true explanation, and there is no reason why the others should not give rise to a very low calculated probability, and so be rejected. So this interpretation cannot be right either.

Once again, we are left to guess at what Dembski really means. From the way his passage above is phrased, it sounds very much like the LCI is intended to be equivalent to his chance-elimination method of inferring design. This would have been the case if he had written that design should be inferred unless the LCI's formula obtains for at least one relevant chance hypothesis. But, if this is what he meant, then the LCI is just a disguised form of his chance-elimination method. What purpose, then, does it serve, except to cause confusion?

Let us move on from the LCI to specified complexity. Despite the clear statement above that for assessing specified complexity we must calculate the probability with respect to all relevant chance hypotheses (probability distributions), Dembski then proceeds to equivocate. In my critique, I listed several assertions by Dembski which support a uniform-probability interpretation (critique section 6.3, exhibits #1 to #4). Dembski now makes feeble attempts to address my exhibits #2 to #4, but only adds to the confusion.

To remind the reader, exhibits #2 and #3 were concerned with programs which regularly produce specified results (solutions to the problem). Therefore, with respect to the hypothesis that the results were produced by the program, they have a high probability, and that hypothesis is therefore not rejected. This hypothesis, which we know to be the true one, must surely be a "relevant" one. According to the chance-elimination method and to Dembski's account above, specified complexity is indicated only if the probability is low with respect to each relevant chance hypothesis (probability distribution). In this case it is not, so the results do not exhibit specified complexity. Yet Dembski claimed they do. What does he have to say on the subject now?

Dembski: One clarification about uniform probabilities in the context of evolutionary computation is worth making here. When I refer to specified complexity in relation to evolutionary computation, I usually intend the complexity to correspond to the probability of the target induced by the natural topology on the configuration/search space in question. Often this is a uniform probability, but it needn't be.

This "clarification" is exceptionally evasive, even by Dembski's standards. He continues to insist that search spaces come with a probability distribution attached, although I challenged this assertion in my critique and he has not responded to my challenge. He does not tell us how to determine what this probability distribution is, merely saying that it is "often" a uniform distribution. He says that he "usually" bases specified complexity on this distribution, but does not tell us why he does so, nor under what conditions he would choose to use some other distribution instead. Most importantly, he fails to explain why he is not calculating the probability with respect to all relevant chance hypotheses, as he told us to above, or, alternatively, why the true explanation is not a relevant chance hypothesis.

On exhibit #4, the SETI sequence, Dembski writes:

Dembski: In many contexts the uniform probability distribution is a good way to see whether we're in a small probability ball park. For instance, I regularly cite the Contact example in which a long sequence of prime numbers represented as a bit string comes from outer space and convinces SETI researchers of the reality of extraterrestrial intelligence. What probabilities might reasonably be assigned to that sequence? What are the relevant chance hypotheses that might assign these probabilities? It's not simply going to be a uniform probability (1s vastly outnumber 0s in representing that sequence). Yet the uniform probability is much more in the right ball park than a probability that concentrates high probability on this sequence.

Again, Dembski is extraordinarily evasive. He stated in No Free Lunch that the SETI sequence exhibits specified complexity, so he needs to show that the probability is low under all relevant chance hypotheses. He tells us that a uniform probability distribution (conferring equal probabilities on the digits 1 and 0) is not quite the right one because "1s vastly outnumber 0s in representing that sequence". Logically, then, we should consider a distribution which corresponds to the actual proportions of 1s and 0s in the sequence, as I suggested in my critique. This means assigning the probabilities 1102/1126 and 24/1126 to the digits 1 and 0 respectively, since we observed 1102 1s and 24 0s. But, under this hypothesis, the probability was 3.78 × 10^-51, not low enough to reject the chance hypothesis, at least with a universal probability bound. As well as ignoring this relevant chance hypothesis, Dembski failed to provide a proscriptive generalization to rule out any other chance hypotheses. So it seems he was not even attempting to consider all relevant chance hypotheses, but thought it sufficient to consider just one, though he doesn't tell us just what that hypothesis is, what probability it conferred on the sequence, or what probability bound he compared it to. Once again, he did not respond to my argument.

Why does Dembski persistently equivocate about this? Does he think there is some tactical advantage in keeping his critics guessing?

5.2 The No Free Lunch Theorems

In my critique section 5.4, I first showed that the NFL theorems do not apply to coevolutionary systems such as biological evolution. Dembski has not even attempted to address that argument.

I then argued that, even for those evolutionary algorithms to which they do apply, the NFL theorems do not support Dembski's fine-tuning claim, because the theorems assume that all mathematically possible fitness landscapes are equally likely, but the existence of regular laws makes this assumption unrealistic. In my previous section (critique section 5.3), I had provided a quotation which makes a similar point:

In spite of the correctness of this "no-free-lunch theorem" (Wolpert and Macready 1997) the result is not too interesting. It is easy to see, that averaging over all different fitness functions does not match the situation of black-box optimization in practice. It can even be shown that in more realistic optimization scenarios there can be no such thing as a no-free-lunch theorem (Droste, Jansen, and Wegener 1999). [Thomas Jansen, "On Classifications of Fitness Functions", 1999]

Dembski's only response to my argument is to point out that not all real fitness landscapes are smooth, citing as examples landscapes based on small changes to written language and computer source code. This may be true (though even the cited landscapes have smooth gradients in places), but it is irrelevant. My argument only requires that smooth gradients be significantly more probable in the presence of regular laws than if drawn randomly from the set of all mathematically possible fitness landscapes. I did not claim, as Dembski writes, that "the laws of nature guarantee the continuity that permits the Darwinian mechanism to flourish". In the hope of avoiding such misunderstandings, I even added the following disclaimer, which Dembski seems not to have read:

Wein: Although it undermines Dembski's argument from NFL, the regularity of laws is not sufficient to ensure that real-world evolution will produce functional complexity.

Nevertheless, I can see now that I made my argument more complicated than necessary. There was no need to mention the subject of "smoothness" at all. So I now offer the following improved text, to replace the second half of my critique section 5.4, from the paragraph beginning "Moreover...":

Moreover, NFL is hardly relevant to Dembski's argument even for the simpler, non-interactive evolutionary algorithms to which it does apply (those where the reproductive success of individuals is determined by a comparison of their innate fitness). NFL tells us that, on average, a search algorithm will perform no better than random search if the fitness landscape is selected at random from the set of all mathematically possible fitness landscapes. Since, in practice, we observe that evolutionary algorithms tend to perform much better than random search, Dembski argues that the selection of fitness landscape must have been biased in favour of good performance by an intelligent designer. But this does not follow. The alternative to design is not random selection from the set of all mathematically possible fitness landscapes. Fitness landscapes are determined at least in part by rules (whether imposed by humans or by the laws of nature), not generated randomly. Rules inevitably give rise to patterns, so that patterned fitness landscapes will be favoured over totally chaotic ones. Thus, the assumption on which NFL is based does not obtain in practice, and NFL therefore cannot be used to support Dembski's conclusion. The fact that NFL does not apply to real situations has already been noted above (see the quotation from Jansen).

Dembski might respond that some sets of rules would produce patterned fitness landscapes but not landscapes conducive to evolution. This is true, but it is no longer an appeal to NFL. It is an appeal to the rules being the right sort of rules for evolution. We do not need NFL to tell us that some sets of rules would not be conducive to evolution. Indeed, we can see some obvious examples. The rules mapping English text to meaning are not conducive to evolution of meaningful texts by substitution of single letters. Where the rules are invented by intelligent agents, as in this case, they may or may not be conducive to evolution. In neither case does this support the claim that an intelligent agent is necessary. If, on the other hand, Dembski considers situations where the relevant rules are the laws of nature (or simulations of them), he is making a variant on the argument from cosmological fine-tuning, arguing that natural laws are more conducive to evolution than could be expected by chance. But what does this add to the existing cosmological fine-tuning argument? At most it would show that natural laws are even more fine-tuned than was previously claimed, and Dembski has not even made that case. He would need to show that fitness landscapes are more conducive to evolution than can be accounted for by the currently claimed examples of fine-tuning.

Next, Dembski appeals to a quote from Geoffrey Miller on how carefully programmers must select the fitness function of an evolutionary algorithm. Since he had already used this quote in a previous article, I foresaw that he might introduce it, and pre-empted him by giving the quotation myself and showing that Dembski had misinterpreted it (critique section 5.2). He appears not to have noticed. And elsewhere I discussed an example where the programmers did not carefully select the fitness function at all, instead using a perfectly obvious one: Chellapilla and Fogel's checkers-playing program (critique section 6.6). Again, no response from Dembski.

Having failed to establish any good reason why the fitness landscapes for biological organisms should not be conducive to evolution, Dembski switches to demanding that biologists explain why they are so conducive:

Dembski: Given, for the sake of argument, that Darwinism is the means by which biological complexity emerged, why is nature such that the fitness landscapes operating in biology are smooth and allow the Darwinian mechanism to be successful?

My critique only set out to refute Dembski's arguments, not to make the case for evolution. Nevertheless, I did briefly address this question (critique section 5.2):

Wein: In the case of biological evolution, the situation is somewhat different, because the evolutionary parameters themselves evolve over the course of evolution. For example, according to evolutionary theory, the genetic code has evolved by natural selection. It is therefore not just good luck that the genetic code is so suited to evolution. It has evolved to be that way.

This is referred to more generally in the literature as "the evolution of evolvability", a subject which Dembski fails to consider at all.

5.3 Specification

Dembski: As is so often the case with Wein's critique, he conveniently omits the key the unlocks the door. Nowhere in his review does he mention the tractability condition, and yet it is precisely that condition that circumvents his worry of artificially tailoring patterns to events. He's right to stress this concern, but I stress it too in NFL and I'm at pains to show how this concern can be met. The way I meet it is through what I call the tractability condition (why no mention in Wein's critique?).

Dembski did not read my critique carefully enough. Let me first quote a sentence from No Free Lunch:

Dembski [NFL]: The tractability condition employs a complexity measure φ that characterizes the complexity of patterns relative to S's background knowledge and abilities as a cognizer to perceive and generate patterns. (NFL, p. 76).

In my critique section A.2, I devoted several paragraphs to discussion of this complexity measure and its use in determining specificational resources. I even quoted the sentence above, less the first four words. In other words, I discussed the tractability condition in all but name. I felt the introduction of yet another term to the discussion was unhelpful, especially one whose name is a hangover from its old use in The Design Inference, and does not reflect its new use in No Free Lunch. I also stated very clearly that specificational resources help to compensate for the tailoring of the specification to the observed event.

Having erroneously accused me of not addressing his argument, Dembski then proceeds to ignore all of my arguments about his statistical method. The one thing he does do is introduce a new, fourth complexity measure, based on "levels" to add to the three complexity measures he mentioned in No Free Lunch (critique section A.2). Which of these four measures should we use? Do we have a free choice?

5.4 Algorithmic Information Theory

Dembski: Wein attributes confusion to me about algorithmic information theory, but the confusion is his. The reason Wein is confused is because within algorithmic information theory, the highly incompressible bit strings are the ones with "high complexity." Thus when I attribute specified complexity to highly compressible bit strings, he thinks I'm confused. But that's because he is reading in his own preconceptions rather than applying the framework I lay out in NFL.

Confusion abounds because of Dembski's conflation of improbability with complexity, and his failure to state which chance hypotheses his improbability-cum-complexity is relative to (critique sections 3.7 and 6.3). He now introduces the terms "probabilistic complexity" and "patterned complexity". Why not just call these "improbability" and "complexity" respectively, like everyone else does? Because it would mean abandoning an important part of the disguise for his argument from ignorance.

He writes nothing in this section to clarify the issue of chance hypotheses, failing to mention them at all except for a passing reference to "coin tosses", which once again suggests that he is considering only a uniform probability distribution instead of considering all relevant chance hypotheses. In my critique, I discussed the relationship of algorithmic information to uniform-probability specified complexity (critique section 6.7), a discussion which Dembski has not addressed. I will now discuss its relationship to eliminative specified complexity.

Consider, for example, the following sequence:

111111111111111111111111111111111111111111111111111111111...

This is a highly compressible sequence, i.e. it has very low algorithmic information (or Kolmogorov complexity). But does it exhibit eliminative specified complexity? That depends on which chance hypotheses we consider to be "relevant". The sequence is "probabilistically complex" with respect to the hypothesis that the digits were generated independently with equal probability (1/2) of being 0 or 1 (a uniform probability distribution). But it is not "probabilistically complex" with respect to a process which outputs a 1 every time; or a process which outputs a 1 with probability 0.9999; or a process which outputs a 0 or 1 (with equal probability) for the first digit, and then repeats the same digit; etc. Thus, the sequence may or may not exhibit specified complexity, depending on whether the processes just listed constitute "relevant" chance hypotheses given our knowledge of the situation.

For an example where Dembski himself attributes specified complexity to such a simple sequence, consider the Caputo case, where he inferred design in this sequence:

DDDDDDDDDDDDDDDDDDDDDDRDDDDDDDDDDDDDDDDDD

Dembski does not explicitly state that this sequence exhibits specified complexity, but he reaches step #8 of the General Chance Elimination Argument (NFL, p. 82), and this step tells us that the observed outcome (E) exhibits specified complexity (p. 73). Since Dembski inferred design when 40 out of 41 draws were Ds, he would have had even more reason to infer design if all 41 draws had been Ds. Thus, a sequence of 41 Ds would also have exhibited specified complexity. This sequence is analogous to the sequence of 1s given above, so we see that such repetitive sequences can exhibit specified complexity. (The Caputo case was based on a local probability bound, but we can imagine extending the sequence to 500 Ds, to reach the universal probability bound.)

We can now see that Dembski's concept of specified complexity is quite different from that of Orgel and Davies, although he persistently conflates his with theirs. As we have just seen, highly compressible patterns can exhibit specified complexity in Dembski's sense. But, in the work of Orgel and Davies, it is incompressible patterns which exhibit specified complexity. I made this point in my critique (critique section 6.7), but Dembski has not responded.

Instead, he gives us a red herring. He reminds us that we must consider all outcomes matching a specification, and not just the observed outcome, implying that I had overlooked this point. I had not. I made the point frequently throughout my critique. In the examples above we can consider the specifications to be "a sequence of all 1s" and "a sequence of all Ds" (see the Caputo case, p. 81). In such cases the specification corresponds to only a single outcome, just as in Dembski's Champernowne (pp. 16-18) and SETI (pp. 143-144) cases. Alternatively, if 1s have no special significance over 0s, we might consider the specification "all digits the same", which corresponds to two outcomes ("1111111111..." and "0000000000..."); this will not significantly alter the probabilities. (Incidentally, Dembski refers here to the "patterned complexity" of a specification, but he has still not unambiguously defined this concept; see critique section A.2.)

I wonder whether Dembski would like to reconsider his insistence that he is not confused about this issue, because the alternative is that his conflation is a deliberate ploy to mislead his readers.

5.5 Predictive Power of Darwinian Evolution

Dembski describes as nonsense my claim that there is a high degree of congruence between phylogenetic trees derived from morphological studies and from independent molecular studies, citing Simon Conway Morris, who writes: "Constructing phylogenies is central to the evolutionary enterprise, yet rival schemes are often strongly contradictory. Can we really recover the true history of life?"

This is an example of the quote-mining tactic which plays such a central role in antievolutionist rhetoric. Indeed, this quotation appears in the Discovery Institute's compendium of mined quotes "Bibliography of Supplementary Resources For Ohio Science Instruction". A quote is provided which superficially appears to support one's position, but significant context is omitted and contrary evidence is conveniently ignored. Here Dembski simply ignores the evidence I cited ("The One True Phylogenetic Tree") and omits to mention that Conway Morris was referring only to the earliest organisms, in the Precambrian and Cambrian periods, where phylogenies are tentative and complicated by lateral gene transfer. The fact that these tentative phylogenies contain some contradictions does not negate my example. I foresaw this sort of spurious objection, and wrote in a footnote:

Wein: It will do Dembski no good to point out that there are a few exceptions to this congruence. The methods for establishing phylogenetic trees are fallible. The prediction is only that there will be a high degree of congruence, not perfect congruence.

Incidentally, since Dembski considers Conway Morris such an authority, I assume he will agree with the following passage from the same paper:

Cooption is, therefore, commonplace (e.g., Finkelstein and Boncinelli, 1994; Holland and Holland, 1999), perhaps ubiquitous, and just what we would expect in organic evolution. ["Evolution: Bringing Molecules into the Fold", Simon Conway Morris, Cell, Vol. 100, 1-11]

5.6 Explanatory Power

Since I confessed myself unable to find a satisfactory definition of "explanatory power", Dembski criticizes me for not consulting the literature. He then proceeds to quote a definition from the literature which is both trivial and question-begging: "Explanations are also sometimes taken to be more plausible the more explanatory 'power' they have. This power is usually defined in terms of the number of things or more likely, the number of kinds of things, the theory can explain. Thus Newtonian mechanics was so attractive, the argument goes, partly because of the range of phenomena the theory could explain."

It is hardly very enlightening to say that the theory with the most explanatory power is the one which can explain the most. This definition simply begs the question of what it means for a theory to explain something. The simplest (but not fully satisfactory) definition of "explain" is that a theory explains a phenomenon if the phenomenon can be deduced from the theory (together with auxiliary theories and initial conditions). This is the "retrodictive" meaning which I gave in my critique. With this meaning, as I pointed out, the intelligent design hypothesis has zero explanatory power.

I note that, except for a little unsuccessful nitpicking, Dembski has made no challenge to my arguments showing that evolutionary theory is superior to the design hypothesis in terms of productivity as a research program, falsifiability, parsimony, predictive power and explanatory power (critique section 7.2).

5.7 Wein's Acknowledgment

Dembski: Wein offers the following acknowledgment for help on his critique of NFL: "I am grateful for the assistance of Wesley Elsberry, Jeffrey Shallit, Erik Tellgren and others who have shared their ideas with me." Am I to assume that Wein speaks for Elsberry, Shallit, Tellgren, and others...?

Of course not.

6. Conclusion

My critique has received no serious challenge from Dembski, and its conclusions remain well-founded.