Specificity
In a more recent paper, Dembski provides an account which he claims is simpler and adheres more closely to the theory of statistical hypothesis testing as formulated by Ronald Fisher. In general terms, Dembski proposes to view design inference as a statistical test to reject a chance hypothesis P on a space of outcomes Ω.
Dembski's proposed test is based on the Kolmogorov complexity of a pattern T that is exhibited by an event E that has occurred. Mathematically, E is a subset of Ω, the pattern T specifies a set of outcomes in Ω and E is a subset of T. Quoting Dembski
Thus, the event E might be a die toss that lands six and T might be the composite event consisting of all die tosses that land on an even face.
Kolmogorov complexity provides a measure of the computational resources needed to specify a pattern (such as a DNA sequence or a sequence of alphabetic characters). Given a pattern T, the number of other patterns may have Kolmogorov complexity no larger than that of T is denoted by φ(T). The number φ(T) thus provides a ranking of patterns from the simplest to the most complex. For example, for a pattern T which describes the bacterial flagellum, Dembski claims to obtain the upper bound φ(T) ≤ 1020.
Dembski defines specified complexity of the pattern T under the chance hypothesis P as
where P(T) is the probability of observing the pattern T, R is the number of "replicational resources" available "to witnessing agents". R corresponds roughly to repeated attempts to create and discern a pattern. Dembski then asserts that R can be bounded by 10120. This number is supposedly justified by a result of Seth Lloyd in which he determines that the number of elementary logic operations that can have been performed in the universe over its entire history cannot exceed 10120 operations on 1090 bits.
Dembski's main claim is that the following test can be used to infer design for a configuration: 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
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