There is a target pattern T that applies to the configuration and whose specified complexity exceeds 1. This condition can be restated as the inequality Dembski's explanation of specified complexity Dembski's expression σ is unrelated to any known concept in information theory, though he claims he can justify its relevance as follows: An intelligent agent S witnesses an event E and assigns it to some reference class of events Ω and within this reference class considers it as satisfying a specification T. Now consider the quantity φ(T) × P(T) (where P is the "chance" hypothesis): <blockquote> Think of S as trying to determine whether an archer, who has just shot an arrow at a large wall, happened to hit a tiny target on that wall by chance. The arrow, let us say, is indeed sticking squarely in this tiny target. The problem, however, is that there are lots of other tiny targets on the wall. Once all those other targets are factored in, is it still unlikely that the archer could have hit any of them by chance? In addition, we need to factor in what I call the replicational resources associated with T, that is, all the opportunities to bring about an event of T'''s descriptive complexity and improbability by multiple agents witnessing multiple events. </blockquote> According to Dembski, the number of such "replicational resources" can be bounded by "the maximal number of bit operations that the known, observable universe could have performed throughout its entire multi-billion year history", which according to Lloyd is 10120. However, according to Elsberry and Shallit, "[specified complexity] has not been defined formally in any reputable peer-reviewed mathematical journal, nor (to the best of our knowledge) adopted by any researcher in information theory." 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 1020 patterns described by four basic concepts or fewer, and so his test for design will apply if 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