Editing Specified complexity (section)

===Calculation of specified complexity===

Thus far, Dembski's only attempt at calculating the specified complexity of a naturally occurring biological structure is in his book ''No Free Lunch'', for the [[bacterial flagellum]] of [[E. coli]]. This structure can be described by the pattern "bidirectional rotary motor-driven propeller". Dembski estimates that there are at most 10<sup>20</sup> patterns described by four basic concepts or fewer, and so his test for design will apply if

:<math> \operatorname{P}(T) < \frac{1}{2} \times 10^{-140}. </math>

However, Dembski says that the precise calculation of the relevant probability "has yet to be done", although he also claims that some methods for calculating these probabilities "are now in place".

These methods assume that all of the constituent parts of the flagellum must have been generated completely at random, a scenario that biologists do not seriously consider. He justifies this approach by appealing to [[Michael Behe]]'s concept of "[[irreducible complexity]]" (IC), which leads him to assume that the flagellum could not come about by any gradual or step-wise process. The validity of Dembski's particular calculation is thus wholly dependent on Behe's IC concept, and therefore susceptible to its criticisms, of which there are many.

To arrive at the ranking upper bound of 10<sup>20</sup> patterns, Dembski considers a specification pattern for the flagellum defined by the (natural language) predicate "bidirectional rotary motor-driven propeller", which he regards as being determined by four independently chosen basic concepts. He furthermore assumes that English has the capability to express at most 10<sup>5</sup> basic concepts (an upper bound on the size of a dictionary). Dembski then claims that we can obtain the rough upper bound of

:<math> 10^{20}= 10^5 \times 10^5 \times 10^5 \times 10^5 </math>
for the set of patterns described by four basic concepts or fewer.

From the standpoint of Kolmogorov complexity theory, this calculation is problematic. Quoting Ellsberry and Shallit{{sfn|Elsberry|Shallit|2003|p=12}} "Natural language specification without restriction, as Dembski tacitly permits, seems problematic. For one thing, it results in the [[Berry paradox]]". These authors add: "We have no objection to natural language specifications per se, provided there is some evident way to translate them to Dembski's formal framework. But what, precisely, is the space of events Ω here?"