Dembski: Building a Better Definition of Intelligent Design

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Here is @Giltil’s example (@93) reworked. I’m going to put this up without further comment until people can look at it help me fix any mistakes. :slight_smile:

According to Dembski:
SC (E ) = I (E) – K (E ) ≥ I (E) – |D |
With
E, the event in question
SC: specified complexity
I: Shannon information
K: Kolmogorov Information
D: description of E
|D|: the number of bits making up D

Here the event (E) in question is event a random sequence generated as a random number with 150 digits of precision from a discrete uniform probability distribution. This sequence of numbers below, represented as a decimal S:

S=0.3702698541 3702698541 3702698541 3702698541 3702698541 0.3702698541 3702698541 3702698541 3702698541 3702698541 0.3702698541 3702698541 3702698541 3702698541 3702698541 (spaces for readability)

and the Event E and probability is defined as:
P[S=0.3702698541 … ] = 10^-150
and 10^-150 = 2^-498.2892142, or I(E) = 499 bits (rounded up) in Dembski’s notation.

Note: For any discrete uniform distribution I(E) simplifies to 1/p, where p is the probability of any given event. For any other distribution I would need to use the formula to calculate the average -log(p_i) for all events.

The number S comes from repeating a randomly generated sequence of digits (“3702698541”) 15 times. It is not irrational or easily described as a fraction, but there is an simple way to compress it. This sequence can be described with the following pseudocode algorithm D such that:

K = 0
FOR i = 0 TO 140 BY 10
  K = K + 0.3702698541 * 10^-i
NEXT i
(See comment @115 for a detailed step-thru)

Accordingly, |D| is 44 characters. Assuming ASCii code characters require 8 bits each, and 44 \times 8 = 352 \ bits (ignoring spaces).

So SC(E) ≥ 499 - 352 = 147 bits

And Dembski’s conclusion would be …

This is a high level of SC. Therefore, chance can confidently be eliminated to explain E.

(Anyone see bugs here?)

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