Introduction. In the beginning of March 2005 William Dembski sent an email message to several critics of his output, including me. Dembski wrote:
Attached is a paper that fills in the details of chapter 4 of No Free Lunch, which David Wolpert referred to as âwritten in jello.â The key result is a displacement theorem. Along the way I prove and (sic) measure-theoretic variant of the No Free Lunch theorems.â
Dembski concluded his message as follows:
ââ¦ I expect that Ken Millerâs public remarks about intelligent design being a âtotal, dismal failure scientificallyâ will become increasingly difficult to sustain. This paper, and subsequent revisions, can be found on my website www.designinference.com. I welcome any constructive comments about it.â
Dembskiâs new paper (in PDF format) is found at http://www.designinference.com/docu[…]e_Spaces.pdf, where its text has already undergone some modifications compared to its initial version. Perhaps these modifications were prompted by critical comments that appeared on the internet, in particular those made by a contributor to the ARN website who signs his posts as RBH, as well as by Tom English and David Wolpert (whose remarks appeared on a certain internet forum).
In his essay at http://www.designinference.com/docu[…]Backlash.htm Dembski wrote,
âIâm not going to give away all my secrets, but one thing I sometimes do is post on the web a chapter or section from a forthcoming book, let the critics descend, and then revise it so that what appears in book form preempts the criticsâ objections. An additional advantage with this approach is that I can cite the website on which the objections appear, which typically gives me the last word in the exchange. And even if the critics choose to revise the objections on their website, books are far more permanent and influential than webpages.â
While Dembskiâs frank admission of the tricks he resorts to in order to âwinâ the cultural war may sound commendable, the tricks themselves are hardly in tune with what normally is considered intellectual integrity. He should have added that making the described revisions in his texts, he usually does not acknowledge the input from critics.
While I make a note of Dembskiâs invitation to offer âconstructive comments about it,â it seems proper to point out that Dembskiâs earlier rendition of the topics covered in his new paper have been extensively discussed and critiqued but he has not deemed it necessary to respond to critique. In particular, in a chapter which I authored in the anthology Why Intelligent Design Fails (editors Matt Young and Taner Edis, Rutgers Univ. Press, 2004) I specifically addressed Dembskiâs [mis]interpretation of the No Free Lunch theorems and his âdisplacement problemâ as it was rendered in chapter 4 of his No Free Lunch book. Dembskiâs new paper in no way answers my critique of his earlier output where he discussed the same notions in a less mathematical rendition. None of my earlier critical comments regarding Dembskiâs misinterpretation and misuse of the NFL theorems and his displacement problem (in its original presentation) is deflected by anything in his new paper.
Iâll try to answer the question - does Dembskiâs new paper justify his assertion that
âKen Millerâs public remark about intelligent design being a âtotal, dismal failure scientificallyâ will become increasingly difficult to sustainâ?
Not quite consistent. In the same vein as my chapter in the anthology Why Intelligent Design Fails, Iâll discuss Dembskiâs new paper without delving into mathematical symbolism as this essay is addressing a general audience rather than only mathematically prepared readers.
Dembski states in his new paper that it mathematically formalizes the ideas previously outlined in a less rigorous form in chapter 4 of his book No Free Lunch (in his words, his new paper âfills in the details of chapter 4 in No Free Lunchâ).
This statement seems to be, first, aimed at asserting the supposed consistency of Dembskiâs discourse, and, second, at providing a sort of answer to the well known characterization (by David Wolpert) of Dembskiâs treatment of the No Free Lunch theorems as âwritten in jelloâ ( www.talkreason.org/articles/jello.cfm). Wolpert is a co-originator of the No Free Lunch theorems, hence his opinion of Dembskiâs treatment of these theorems carried considerable weight. Some of Dembskiâs admirers tried to play down the significance of Wolpertâs critique by posting letters to that effect on various internet fora. However, Dembski himself has maintained a deafening silence, as if Wolpertâs critique did not exist. It seems that the statement in his new paper which points to the supposed consistency between chapter 4 in his 2002 book and his new paper is a device designed to blunt the sharpness of Wolpertâs characterization.
However, the comparison of Dembskiâs new paper with chapter 4 in his book shows that the assertion of consistency is not quite true. In fact, Dembskiâs new paper introduces certain substantial modifications of the basic concepts suggested in the âjelloâ chapter in his earlier book. The displacement problem No 1 (as rendered in the No Free Lunch book) and the displacement problem No 2 (as discussed in the new paper) seem to be not quite the same problem (as Iâll discuss below), although Dembskiâs position is that the two displacement problems are identical.
Dembskiâs new paper is heavily mathematical and is obviously designed to impress readers with his mathematical sophistication. Dembskiâs colleagues (some of whom may even not have a proper background to comprehend his mathematical ruminations) have promptly acclaimed this new paper as âsplendidâ and allegedly âdisplacingâ that perfidious offshoot of materialistic philosophy, âDarwinism.â
I believe the delight of Dembski and his colleagues is premature.
Fallacious assumptions. First a very general observation. Dembskiâs delight is based on the implicit assumption that fundamental concepts of biological science can be âprovedâ or âdisprovedâ mathematically. Dembski has adhered to similar notions previously, for example, suggesting in his book The Design Inference that representing certain notions in a mathematically symbolic form somehow âprovesâ them. In my book Unintelligent Design (chapter 1, pages 26-28) I have demonstrated the fallacy of such a supposition, using as an example Dembskiâs presentation of an argument for design in two versions - once expressed in plain words, and once in a mathematically symbolic form. As is evident from that juxtaposition of two renditions of the same argument, using mathematical symbolism does not provide any additional insight and, in Dembskiâs case, only served to embellish his discourse. In his recent papers, including the paper I am discussing here, Dembski makes a further step on the same road. Now his overall approach seems to be implicitly based on the idea that a purely mathematical discourse is capable of âdisplacing Darwinism.â Of course, this is wishful thinking. âMathematics is a language,â said the great American physicist Josiah Willard Gibbs. Indeed. Mathematics is an extremely powerful tool. However, no mathematical theorem or equation âprovesâ or âdisprovesâ anything beyond the logical connection between a premise and a conclusion. If a premise is false, so is the conclusion, regardless of how sophisticated and impeccably correct the applied mathematical apparatus is. Since Dembskiâs proclaimed goal is to prove âDarwinismâ false, all of his mathematical exercise is irrelevant as it in principle cannot achieve such a goal. Evolutionary biology is an experimental science and âDarwinianâ mechanisms of evolution have been supported by an immense empirical material. No mathematical theorems or equations can âdisplaceâ evolutionary biology. Its successes and failures can only stem from empirical research and observations bolstered by proper theorizing, wherein mathematics, however important and enlightening, is always only a tool.
Closely connected to this fallacious approach to mathematics as allegedly capable of âdisprovingâ evolution, there is another serious (I would say fatal) drawback to Dembskiâs approach. He seems to first implicitly define his goal (in this case to prove that âDarwinianâ mechanisms cannot explain evolution) and then apply what is an analog of âreverse engineeringâ to find a premise from which his already chosen conclusion can be mathematically derived. The premise deliberately chosen to lead to a pre-determined conclusion has little chance to be true.
Dembskiâs premise. To be more specific, let us see what Dembskiâs premise implies. Here there is indeed a certain consistency between his earlier discourse in his No Free Lunch book and his new paper. He considers biological evolution as the search for a certain small target within a very large search space (which in his book was referred to as the âphase spaceâ).
As I pointed out in Why Intelligent Design Fails, in his No Free Lunch book Dembski did not suggest a definition of a target. In his new paper this lacuna has been filled. Now Dembski provides a definition of a target. Without delving into Dembskiâs mathematical formalism, he defines target T as a particular small region somewhere within the very large search space Q. He asserts next that finding the target using a blind search is an endeavor whose success has a very small probability. For the search to be successful, it has to be âassisted,â which means the search algorithm needs to get information about the structure of the search space. For example, the search algorithm may be assisted by feedback, letting the algorithm know whether each step brings it closer to the target or pushes it farther from the target. The source of such information lies in a âhigher-orderâ information space. In Dembskiâs No Free Lunch this higher-order space was denoted J. From that earlier discourse seemed to follow that space J contained (perhaps besides some other things) all possible fitness functions. In his new paper the âhigher-orderâ space is denoted M and seems now to contain not the fitness functions but rather all possible âsearches,â that is all possible search algorithms. This seems to be a substantial change of the entire concept of the âdisplacement problemâ which Dembski claims to be the main element of his discourse. It seems to be at odds with Dembskiâs claim asserting that his new paper is just âfilling in detailsâ in his earlier rendition of his ideas, this time on a more rigorous level, so it is no longer âwritten in jello.â In fact, his new rendition is substantially different from the original version found in his book.
Dembskiâs assisted searches and NFL regress. Let us recall once again the problem Dembski discusses in his new paper. It is a search for a small target within a large search space. Mathematically analyzing this problem, Dembski concludes that only an âassisted searchâ has a reasonable chance of success and such an âassisted searchâ is only possible if, first, a âsearch for a searchâ is conducted in a higher-order information-resource space. The latter, however, in turn requires information from an even higher-order space, etc. Dembski calls this situation âNo Free Lunch Regress.â He maintains that âstochastic processesâ (and biological evolution belongs in this category) are incapable of getting out of the regress in question, so for the search to be successful, input from intelligence is necessary (which seems to be in fact his a priori conviction, just not expressed explicitly). Dembskiâs claim that the âassistanceâ can only come from an intelligent source reflects his antecedent belief but is not supported by any argument, either mathematical or heuristic. A detailed discussion of this point is not necessary, however, because, as I will show, Dembskiâs entire schema is irrelevant for real-life searches. Another comment that immediately comes to mind is that if a search is assisted by information from a higher-order space, the search algorithm that has acquired such information is not a âblack-boxâ algorithm any more, so the No Free Lunch theorems, at least in the form they were proven by Wolpert and Macready, are invalid for such algorithms. (Wolpert-Macreadyâs proof was valid for black-box algorithms. A black-box algorithm has no advance knowledge of the fitness landscape and acquires such knowledge step-by-step, extracting it from the fitness landscape in such a way that it accumulates information about the already visited points in the landscape but still has no knowledge of any points not yet visited; it possesses no knowledge of a target either, if the search is target-directed.)
Although this simple consideration casts doubts on Dembskiâs entire discourse (unless he can prove that the requirements for an algorithms to be of a âblack-boxâ variety can be invalidated) it is of a secondary importance because the No Free Lunch theorems are only about the average âperformanceâ of search algorithms and are irrelevant to the actual problem of a specific search algorithm facing a specific fitness landscape. In that, Dembskiâs new paper is not an improvement over his earlier discourse and fails to account for the irrelevance of the NFL theorems for biological evolution.
Moreover, regardless of the NFL theorems, Dembskiâs discourse seems to be, again, irrelevant to real-life problems for a more universal reason. Here is why.
Do we need to analyze all of Dembskiâs convoluted mathematics in order to see whether his conclusion is substantiated? No. There are several reasons to ignore Dembskiâs mathematical exercise but I will now point to only one such reason which, I believe, is fully sufficient to reject Dembskiâs conclusion.
Is biological evolution a search for a target? Biological evolution has nothing to do with the problem Dembski analyzes in his new paper - the problem of a search for a small target in a large search space.
Let us grant Dembski the assumptions and derivations he offered in his mathematical exercise. They may be perfectly correct or partially defective, but either way it will not affect our general conclusion.
Biological evolution is not a search for a target in a search space. It knows of no target. It is blind and its results are not predetermined, unlike the results of a targeted search employed in certain artificially designed evolutionary algorithms (such as in Dawkinsâs âweaselâ algorithm). Look at Dembskiâs example of a âsearchâ for a particular protein. He calculates that the probability of âfindingâ a particular protein which is 100 amino acids in length via a random search in a space of all possible proteins of such a length, assuming uniform distribution of probabilities in this space, is so small ( 10-130 ) as to be practically hopeless. The arithmetic here may be perfectly correct, but it has no relevance to real biological evolution. Evolution does not search for a particular protein determined in advance as a target. It conducts a variety of blind âsearches,â the number of which is immense and some of them result in a spontaneous emergence of certain biologically useful proteins, whose biological role was not foreseen. The probabilities of such occurrences are irrelevant: because of the very large number of such âsearches,â the overall likelihood of emergence of some useful proteins is by many orders of magnitude larger than the number Dembski calculates. Moreover, imposing upon ârandom searchesâ a non-random factor - natural selection may serve as an example of such a non-random factor - drastically accelerates the process. There are other natural factors ignored in Dembskiâs schema which naturally âassistâ the âsearch,â so it is âassistedâ without input from intelligence and without a need to search a âhigher-orderâ space. Dembskiâs model of proteinâs components randomly assembling all at once is very far from realistic scenarios discussed in evolutionary biology. Dembski schema is utterly arbitrary insofar as it relates to a natural biological process.
Therefore all Dembskiâs theorems and equations, as well as his conclusions, have no relevance to evolutionary biology.
Conclusion: is Dembskiâs mathematics relevant to intelligent design? Are Dembskiâs mathematical exercises relevant to intelligent design in general? I donât think so. Indeed, let us assume that Dembskiâs thesis is valid for targeted genetic algorithms like Dawkinsâs âweaselâ algorithm. Even if this is true, it has no relevance to the question of the validity of intelligent design. We know anyway that such artificially designed algorithms receive input from an intelligent agent - a human programmer who supplies âassistanceâ to the algorithm in the way of a feedback: it tells the algorithm at every step of the search whether it comes closer to the target, stays the same distance from it, or moves farther from the target. The same may be true for many other artificially programmed genetic algorithms.
However, this in no way means that an analogous situation exists in the biosphere where the search is not target-oriented and where therefore no input from an âassistingâ agent is required. In fact, in biological evolution no âassistanceâ from a âhigher-orderâ information space is possible because the outcome of a search is not known in advance, so the âsearchâ (if we agree to apply this term, which is in fact a misnomer) is in all cases spontaneous and undirected. All this has no relation to the No Free Lunch theorems, either those for fixed landscapes or those for co-evolution, which all are irrelevant to the actual encounters of specific natural genetic algorithms with specific fitness landscapes, either fixed, or co-evolving in the course of the search. Hence the question of whether Dembskiâs mathematical exercise is formally correct or contains errors is irrelevant to the question of intelligent designâs validity. Even if artificial genetic computer programs indeed require an input from intelligence (although even some of such algorithms work without such an input) this is not a question of concern if intelligent design is discussed. The latterâs validity is predicated upon whether or not intelligent input is required for natural non-targeted searches.
Neither Dembski nor anybody else has so far suggested any evidence that such input is necessary for non-targeted searches. Dembskiâs new paper has not done anything like that by a long shot. In my view this paper is an exercise whose heavy mathematical embellishment serves no other purpose than showing once more that Dembski, on the one hand, knows a lot of mathematical symbols, and on the other hand has problems with overall consistency and logic.
As the matter now stands, Ken Millerâs statement quoted by Dembski remains fully valid. (Besides Miller, it is shared by most scientists who happened to come across Dembskiâs numerous publications - a good example is perhaps the anthology Why Intelligent Design Fails - which Dembski fails to even mention, let alone to reply to). Dembskiâs new mathematical exercise does nothing to make the statement about the abject scientific futility of intelligent design any less true than it has been until now.
PS. I have a surgery scheduled for tomorrow morning, so Iâll be unable to respond to critical comments, if any, at least for a while. MP