Specified complexity: Difference between revisions

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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).<ref>Michael Sipser (1997). ''Introduction to the Theory of Computation'', PWS Publishing Company.</ref> 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

:<math> \sigma= - \log_2 [R \times \varphi(T) \times \operatorname{P}(T)], </math>