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The Behe test refers to the main argument made against Darwinism by the biochemist Michael Behe:
By irreducibly complex I mean a single system composed of several well-matched, interacting parts that contribute to the basic function, wherein the removal of any one of the parts causes the system to effectively cease functioning. An irreducibly complex system cannot be produced directly (that is, by continuously improving the initial function, which continues to work by the same mechanism) by slight, successive modifications of a precursor system, because any precursor to an irreducibly complex system that is missing a part is by definition nonfunctional. An irreducibly complex biological system, if there is such a thing, would be a powerful challenge to Darwinian evolution. Since natural selection can only choose systems that are already working, then if a biological system cannot be produced gradually it would have to arise as an integrated unit, in one fell swoop, for natural selection to have anything to act on.
After giving the example of a mousetrap as an irreducibly complex system, Behe then gives several detailed examples of specific biochemical systems that are irreducibly complex: the cilium; the bacterial flagellum; blood clotting; the immune system’s clonal selection, antibody diversity, and complement system.
By focusing on the issue of irreducibly complex systems, and being clear about that focus, Behe avoids the strong part of Darwinism, which is natural selection, and instead concentrates on the weak part of Darwinism, which states that random physical events are the cause of the changes winnowed by natural selection. Note that the previous section uses as its probability example the DNA needs of the first self-reproducing bacterium, so as to avoid any possible involvement of natural selection.
Calculating the probability for one of the irreducibly complex biochemical systems given by Behe, assuming the system arose by chance, is non-trivial. However, mathematician William Dembski, in his book No Free Lunch, tackles the specific problem of calculating a probability for the formation of a bacterial flagellum by chance. For a bacterium that has one or more flagella, its flagella are a means of moving that bacterium about in its watery environment. Each flagellum has a long whip-like filament that extends outward from the bacterium’s cell wall. This filament is attached to a structure, called a hook, that acts as a universal joint which connects the filament to a specialized structure embedded in the cell wall that acts as a bi-directional motor that can rotate the filament in either a clockwise or counterclockwise direction. Because of the helically wound structure of the filament, one of these rotation directions causes the spinning filament to act like a propeller that pushes the bacterium in one direction, and the opposite rotation causes the spinning filament to act as a destabilizer that causes the bacterium to tumble (the bacterium tumbles when it wants to change the direction it is moving in).
For comparison purposes, Dembski first calculates what he calls a universal probability bound, the idea of which is that anything dependent on chance whose probability is smaller than this universal probability bound is extremely unlikely to happen no matter how much time and material resources in the universe one invokes on the side of chance. His universal probability bound, which is very generous to those who want to invoke Darwinism and its reliance on chance, is computed as follows (1080 is the estimate by physicists of the number of elementary physical particles in the visible universe; 1045 is roughly the number of Planck-time intervals in one second; 1025 is more than ten million times the age of our Milky Way galaxy in seconds):
Thus, given this universal probability bound, anything with a probability less than 10–150 can be safely dismissed as so unlikely that there is no reason to consider it as possible when offering an explanation for the formation of an irreducibly complex biochemical system.
Dembski then defines an equation for the probability of a structure arising by chance. His equation may be written as:
pstructure = poriginate-parts × plocalize-parts × pconfigure-parts
In the above equation, pstructure is the probability of getting either the specified structure or a functionally equivalent structure; poriginate-parts is the probability of originating all the parts that are needed to build an instance of the specified structure or a functionally equivalent structure; plocalize-parts is the probability that the needed parts are located together at the construction site; pconfigure-parts is the probability that the localized parts are configured (assembled) in such a way that either the specified structure or a functionally equivalent structure results.
At this point one may object to the application of the above equation to the structure of a bacterial flagellum, by raising the current assumption in biology that cellular structures such as the bacterial flagellum are completely encoded in the DNA (this encoding is typically assumed to include, in effect, localization and assembly instructions, even though at present the only code in DNA that has been deciphered is the code that specifies the structure of individual proteins). However, even if one grants this current assumption in biology, the above equation is still applicable, because the information content that one then assumes arose by chance in the DNA to fully specify a bacterial flagellum, must overcome whatever random chance events oppose that specification’s realization. In effect, 1 – pstructure is a measure of the random chance events that oppose that specification’s realization. Thus, the imagined specification in the DNA must have a specificational complexity whose probability of arising by chance is similar to the probability pstructure.
In Dembski’s computation of pstructure for a bacterial flagellum, the parts of the structure are individual proteins. For the Escherichia coli bacterium, Dembski refers to the technical literature and says that about 50 different proteins are needed to make the flagellum, with about 30 different proteins being in the final form of the flagellum, including:
The filament that serves as the propeller for the flagellum makes up over 90 percent of the flagellum’s mass and is comprised of more than 20,000 subunits of flagellin protein (FliC). … The three ring proteins (FlgH, I, and F) are present in about 26 subunits each. The proximal rod requires 6 subunits, FliE 9 subunits, and FliP about 5 subunits. The distal rod consists of about 25 subunits. The hook (or U-joint) consists of about 130 subunits of FlgE.
Given these details, Dembski computes plocalize-parts as follows:
Let us therefore assume that 5 copies of each of the 50 proteins required to construct E. coli’s flagellum are required for a functioning flagellum (this is extremely conservative—all the numbers above were at least that and some far exceeded it, for example, the 20,000 subunits of flagellin protein in the filament). We have already assumed that each of these proteins permits 10 interchangeable proteins. That corresponds to 500 proteins in E. coli’s “protein supermarket” that could legitimately go into a flagellum. By randomly selecting proteins from E. coli’s “protein supermarket,” we need to get 5 copies of each of the 50 required proteins or a total of 250 proteins. Moreover, since each of the 50 required proteins has by assumption 10 interchangeable alternates, there are 500 proteins in E. coli from which these 250 can be drawn. But those 500 reside within a “protein supermarket” of 4,289 [different] proteins. Randomly picking 250 proteins and having them all fall among those 500 therefore has probability (500/4,289)250, which has order of magnitude 10–234 and falls considerably below the universal probability bound of 10–150.
For computing probability poriginate-parts, Dembski is willing to concede a value of 1 (certainty) if one wants to assume that the needed proteins are already coded in the bacterium’s DNA for other uses. For computing probability pconfigure-parts, the computational approach used by Dembski is more complex than that used for computing plocalize-parts, but gives a similar result of a probability that is much smaller than his universal probability bound of 10–150.
 Behe, Michael. Darwin’s Black Box. Touchstone, New York, 1998. p. 39.
 Ibid., pp. 59–65.
 Ibid., pp. 69–72.
 Ibid., pp. 79–96.
 Ibid., pp. 120–138.
 Dembski, William. No Free Lunch: Why Specified Complexity Cannot Be Purchased without Intelligence. Rowman and Littlefield Publishers, Lanham Maryland, 2002. pp. 289–302.
 Ibid., pp. 21–22.
 Ibid., p. 291. The pstructure equation is equivalent to—but more descriptively labeled than—the pdco equation given by Dembski.
 The analysis in this paragraph is mine not Dembski’s, because this objection is not dealt with in Dembski’s book No Free Lunch.
 Ibid., p 293.
 Ibid., p 293.