### Is the flagellum complex? Computing the crucial probability.

Following Behe, Dembski describes the bacterial flagellum as an “irreducibly complex system that is unattainable by the Darwinian mechanism.”He then seeks “to show how irreducible complexity is a special case of specified complexity, and ... to sketch how one calculates the relevant probabilities to eliminate chance and infer design for such systems. Determining whether an irreducibly complex system exhibits specified complexity involves two things: showing that the system is specified and computing its probability.... Specification is never a problem.”We will deal with that glib remark about specification shortly, but our immediate concern is with Dembski’s attempt to compute P(flag|N), the probability that E. coli’s flagellum was actualized by the joint action of all relevant natural processes.

Curiously, Dembski not only rejects any proposal consistent with the gradualism that ID presumes to be an essential feature of the Darwinian mechanism, he also effectively ignores the fundamental role that genes play in providing the instructions for the development of cellular structures. Instead, Dembski simply asserts that the probability in question must be computed by treating the bacterial flagellum as a chance-assembled discrete combinatorial object. A discrete combinatorial object (dco) is an object that is composed of particular kinds of building blocks that must first be gathered into one location and then configured in a particular arrangement to form the complete object. According to Dembski, the probability that such an object would form naturally is the product of three distinct probability factors. P(dco) = P(orig) x P(local) x P(config) where

P(orig) = the origination probability = the probability that the requisite building blocks for the structure in question will originate, by chance,

P(local) = the localization probability = the chance probability of localizing these building blocks in one place once they become available, and

P(config) = the configuration probability = the chance probability of configuring the building blocks into the particular structure once they are localized.

Dembski repeatedly refers to these probability factors as probabilities that some process (origination, localization, or configuration) will successfully occur “by chance.” Remembering that in ID literature the term “by chance” can mean either “by pure chance” or “by all relevant natural processes,” how can we tell which meaning is here intended? In context, and given Dembski’s repeated references to these same phenomena as being wholly “random” in character, it would appear that the “pure chance” meaning is the primary meaning here intended. Dembski’s method of computation affirms that interpretation.

So, then, we are asked to imagine a bacterial flagellum arising from the pure chance gathering of approximately 50 of the right kinds of proteins (and in the correct proportions) at some spot in the vicinity of the cell wall and plasma membrane of E. coli and then, again by chance, happening to configure themselves into a functioning rotary propulsion system for this bacterial cell.

Not surprisingly, Dembski’s computations and estimations of the three probability factors lead him firmly to the expected conclusion: Considered as a discrete combinatorial object that must self-assemble from the chance localization of the requisite, chance-assembled molecular components, the probability of a flagellum assembling itself and attaching itself to the cell membrane of E. coli is exceedingly small in comparison to the universal probability bound. By Dembski’s measure, it is demonstrable beyond any shadow of doubt that bacterial flagella cannot self-assemble as discrete combinatorial objects.

Note carefully, however, what Dembski has actually done with his probability computation. By his own definition of complexity, the probability value he needs is P(flag|N), the probability that the flagellum could form by the joint action of all relevant natural means. However, given the epistemic limitation we noted earlier, the best he could possibly do would be to compute P(flag|n), the probability that the flagellum could form by the joint action of known natural means. But this is not what he actually computed. What Dembski computed instead is P(flag|dco), the probability that the flagellum could form by pure chance alone as a discrete combinatorial object.

But, of course, no biologist has ever taken the bacterial flagellum to be a discrete combinatorial object that self-assembled in the manner described by Dembski.Dembski has not defeated any actual biological proposition. He has slain nothing more than an imaginary dragon - a fictitious adversary that Dembski himself has fabricated from a stack of rhetorical straw.

E. coli bacteria possess flagella, not because flagella self-assemble and self-attach to the cell membrane, but because the genome of E. coli came to include in its genetic library - the instruction manual that enables the cell to perform a vast number of functional and formational operations - the coded instructions for growing the flagellar propulsion system. That being the case, the question that Dembski needed to deal with was not, Could the flagellum self-assemble as a discrete combinatorial object? but rather, Could that portion of the E. coli genome that codes for the production of a flagellum have come about by natural means?

Stating the question in this manner, however, places Dembski in a difficult and awkward position. The awkward element is simply that he failed to deal with this fundamental question in any substantive way. By focusing his energies on an attempt to compute the mathematical probability that a bacterial flagellum would self-assemble from a highly improbable environment of specialized proteins, Dembski effectively chose to ignore the role of genetics in the formation of biotic systems. That is an astounding choice. But there may be reasons for taking that questionable option. Choosing to deal realistically with the role of genetics would have presented Demski with a formidable menu of strategic difficulties.

The question on the table remains, Could that portion of the E. coli genome that codes for the production of a flagellum have come about by natural means? To answer affirmatively would be to say that the bacterial flagellum was not intelligently designed - that it needed no supplemental, non-natural action to actualize it. The ID movement would then have to abandon the bacterial flagellum as its flagship example of an intelligently designed biotic structure.

To answer negatively, on the other hand, would introduce an equally awkward difficulty. To single out the flagellar portion of the E. coli genome as the only subset of base-pair sequences that required non-natural action to configure them correctly forces that portion into a special category relative to the rest of the genome. Why would the flagellar portion need supplemental non-natural action if the rest of the genome did not? Would that not seem odd? Indeed it would, and Dembski knows it.

We must grant, then, that Dembski expects some non-flagellar portions of the E. coli genome to be equally in need of non-natural configurational action. There is, however, a certain irony here in Dembski’s reasoning. In effect, he is presuming that if designer action (form-conferring intervention by an unidentified and unembodied choice-making agent) is required for configuring what I might call “the flagellar 2%” of the E. coli genome, then a person may reasonably infer that similar designer action was required for forming some portions of the other 98%. Dembski does not offer one iota of supportive empirical evidence for this conjecture. He does not provide even a hint regarding what other structural components of E. coli might need that supplemental designer action. As it stands, Dembski’s position is based on nothing more than a grand extrapolation from one purported “instance” of designer action. How does Dembski justify this sort of unconstrained extrapolation in the face of his claim that the ID perspective is based solidly on scientific evidence and his injunction that, “Science must form its conclusions on the basis of available evidence, not on the possibility or promise of future evidence”?

Interestingly, the E. coli genome does contain genes for the formation of structures remarkably similar to portions of the flagellum system. Bacteria like E. coli possess systems for the secretion of certain proteins from the cytoplasm in the cell interior to the extracellular space beyond, often directly into host cells. Several structures are known to accomplish this secretion function. Of special relevance here is the type III secretion apparatus, composed of about 20 proteins, most of which are homologous to the to components of the flagellar biosynthesis apparatus.To put it as simply as possible, the type III secretion apparatus and the “motor apparatus” of the bacterial flagellum employ similar building blocks and share numerous structural features. Thus, the genetic coding for one of these structures is going to be closely related to the genetic coding for the other.

The question now becomes, What is that relationship? Were these coding sequences independently configured by an intelligent designer? If so, where is Dembski’s “design-theoretic” analysis of the secretion apparatus? If not, how could the coding for the secretion apparatus arise naturally if the coding for the structurally similar flagellum required non-natural configurational action?

We must remember, however, that Dembski did not actually argue for designer action (actualizing particular molecular structures) to configure the genetic codes for either the secretion apparatus or the flagellum His argumentation was instead focused solely on the probability that the flagellum itself could be actualized by the joint action of all natural processes (the “chance hypothesis”). Well, then, suppose that the flagellum really was assembled for the first time by the form-conferring action of an unembodied intelligent designer independently of genomic instructions. Since instructions for the development of flagella are now part of the E. coli genome, are we to believe that the designer added those instructions to the genome as a separate act? Are there two independent form-conferring acts here - one for the first flagellum and another for the genomic instructions to produce all subsequent flagella?

Presumably, Dembski could argue that a single designer-action would be sufficient - infusing the E. coli genome with the genetic information needed to effect the construction of the flagellum. But then the entirety of Dembski’s argument and computation based on treating the flagellum as a chance-assembled discrete combinatorial object would become irrelevant to the question of complexity. Dembski would have to deal openly with the genome and the relationship of its coding for the flagellum with its coding for structurally similar systems like the type III secretion apparatus. In fact, he would have to scrap his original calculation regarding the flagellum as a dco and develop an entirely new genetic approach to computing the probability that the flagellum was formed naturally.

Are the flagella of the E. coli bacteria complex? Dembski thinks so, but his strategy of treating the flagellum as a discrete combinatorial object is far off the mark of demonstrating this. The probability value that he claims to have computed has no biological relevance to the question of how flagella of E. coli bacteria were first actualized.

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