There were several requests on the next-to-last thread for definitions of specified complexity, so to redeem a promise and– I hope–eliminate the need for repeating the same definition ad infinitum, I’ll attempt to summarize the major points of Dembski’s paper on the subject here.


The context dependent measure of specified complexity is given by the following formula:

χ = -log2 [M • N • φs(T) • P(T|H)]

(pg 21)

This is the definition we are using in this course.


M and N represent the replicational resources. In a general case, we may replace them by 10120 (upper bound of bit operations our universe could have accomplished throughout her history) to get
χ = -log2 [10120 φs(T) • P(T|H)]

(pg 24)



Specificity is calculated by means of the following formula
σ = -log2 [ φs(T) • P(T|H)]

(pg 18)

Aside from the ommision of replicational resources (M and N), this formula is identical to the above formula for specified complexity. It is dependent on two components, φs(T) and P(T|H).



φs(T) is defined as a measure of the specificational resources, and is given by the cardinality of {U ∈ patterns(Ω) | φ’s(U) ≤ φ’s(T)} where patterns(Ω) is the collection of all patterns that identify events in Ω. φ’s(T) is the descriptive complexity of T (a measure of the simplest way for s to describe T).

(pg 21)

“S” represents the subject who determines & describes, with the languages available to him, the pattern.

To make this simple, consider the special case where the only language is the language used in programming register machines, and the patterns being described are bit strings. When analyzing a string of a given length, you determine first how long the program describing it must be, and then determine how many other bit strings of that length there are with descriptions at least as short. This second number is equal to φs(T).

In the general case we have many more languages and patterns far more complex than bit strings, but the same concept holds.



P(T|H) is the probablity of pattern T given the relevant chance hypothesis H. P(T|H) ≠ 1 in cases where H, the chance hypothesis, is known, unless H is completely deterministic.

P(T|H) where T=heads and H is a fair coin toss is 1/2.

P(T|H) where T=(heads)(tails)(heads)(tails) and H is a series of independent fair coin tosses is 1/16.



Finally, T is considered a specification if the measure of specified complexity is strictly greater than 1.



Corrections from anyone comfortable with the paper are very welcome. In the meantime…

Michal wrote
Where is the complex specified information defined in a clear fixed unambiguous way, along with all the key sub-terms, Hannah?

Is there anything ambiguous about those definitions?