Dembski: Building a Better Definition of Intelligent Design

[Dan_Eastwood]

@colewd

Gil is referring to specified complexity and Tim is talking about complexity. Tim cited a definition of complexity which maybe different than specified complexity. This discussion has the chance to bear some fruit if definitions can be mutually understood by all.

A reasonable goal, and you give an example that makes a point I need to be sure everyone understands.

Bill’s scenario:

The probability of the result of 500 coin tosses is 1. [I think Bill means “Sum of probabilities”] The probability of a predicted pattern like heads and tails with never [be] 2 heads or tails ie HTHTHTHTHT…500 times is orders of magnitude less than one. If we see this pattern we can eliminate a fair coin or flipping a fair coin as the cause.

Considered as Bernoulli trials, the probability of a sequence “HTHTHTHTHT…” is the same as 500 heads or 500 tails. To get different probabilities we need to redefine this as “a binary sequence of length 500”, which is a different distribution. Let’s define the variable S and the distribution SEQ:

S ~~ SEQ(N,P*)
{read “~~” to say “distributed as”}

is the probability distribution of N characters (H or T, or 1 and 0 in a binary representation), and P* is a vector of 2^N probabilities for each of the 2^N possible sequences. The sum of all P* is 1.0, of course.

If the probabilities in P* are uniform (all equal to 2^-N) then we have the situation where the probabilities are equal under Bill’s scenario.

A sequence of Bernoulli trials is unlikely to generate this alternating sequence. More formally we have rejected the null hypothesis that the HTHTHT sequence was generated using Bernoulli trials. We only have a single observation of S to estimate P[HTHTHT sequence], but (under Bill’s scenario), so we can’t say much about the distribution of S or the probabilities P* without a lot more data - more sequences of length 500.

OK, definition in place, I can make a few statements:

1. Dembski often swaps the Bernoulli trial and “SEQ” distributions to suit the conclusions he wishes to reach. Specifically, he poses the observed results of evolution as a Bernoulli trials, and we know that isn’t right.

2. Bill’s scenario could still be committing the Texas Sharpshooter fallacy. The are MANY patterns of S that would lead us to reject this null.

3. The selection of N=500 is arbitrary. If we choose N=2, then the possible sequences are: HH, HT, TH TT, and all have probability 0.25. IF we define a probability less than 0.1 are “unlikely” or “complex”, then none of these are complex. IF you choose N=4, then all sequences have probability 0.0625, and all are complex. GIven any arbitrary definity of “complex” as a small probability, it is always possible to choose N large enough to reach the conclusion that an observed S is complex.

I wrote about most of this 9 years ago.

More replies later - work to do!