The product M\cdot N \cdot \phi{(T)} is an integer and P(T|H) a probability. Dembski uses this as an approximation for the probability of T occuring. BUT it’s not a probability; it’s the binomial expectation for the number of observed T, and can be greater than one…

I have a blog post about it. Notes on the correct calculation appear near the bottom (in the Addendum).

Thanks for the pointers. I was going to work from Dembski’s CSI criterion (2002) and see how close I could come to deriving the 2005 formula from it. Will get to that.

I spent a lot of time with the 2005 paper, multiple reads reviewing the references. I thought I must be missing something, that Dembski must be doing something I didn’t understand. How else could he have probabilities greater than one? Elberry and Shallit (2011) covered everything else, I’m surprised they missed this.

No doubt he did make that blunder. I would say that Complex Specified Information (a notion not invented by Dembski but by Leslie Orgel, and also used by Jack Szostak and Robert Hazen) is not a senseless notion. It’s just that having it does not prove that something is designed. At Panda’s Thumb I recently posted an argument that using Algorithmic Information Theory in this context is useless. But using a component of fitness does make sense and we can see that lots of adaptations have high specified information. Perhaps we could discuss this in a special thread at PT.

That would be interesting. I’d like to contribute if I can.

A few comments on your post at PT:

If I have to choose, ASC is preferable to CSI because at least the math is correct.

I agree that ASC is not useful for analyzing evolution, at least not in in terms of pure quantity. Extreme large or small amounts of ASC cannot describe a living thing: too simple (a crystal) and it is not alive, too random and it cannot be evolved (I think). What matters is the right amount of informationrelative to fitness in a given environment.

You touch on “complexity of description” not necessarily being related to fitness, which is correct. ASC is built around the concept of a Universal Turing Machine (UTM) with random input. We cannot guarantee a shorter coding for random input, BUT there may exist coding schemes where shorter (or optimal) coding is possible. We could hypothesize a Biochemical Turing Machine (BTM) that incorporates the laws of chemistry. I don’t think this is useful, I’m only suggesting that it should be true.

I agree that variability in the population is necessary part of any description. Conservation of ASC can only hold with respect to a single genotype.

OK, I will work on a short post, with some links to resources. The intent would be to allow you and I and any sensible other commenter to discuss the relationship between Dembski’s use of CSI in 2002 and his Specified Complexity measure in 2005. I am not much interested in further explication of the ASC measures. I appreciate your comments above, but basically have seen no justification from Dembski and Co. of using measures of simplicity of description to say anything about evolution.

You don’t need to be, it’s just Mutual Algorithmic Information with a new name slapped on it. (I think, it’s been some time since I read that paper.)

I don’t have Dembski’s 2002 book, so I can’t help you there. (Is that the version with the “Critical Region”?)

Agreed. The closest Dembski (2005) got was calling P(T|H) the probability of the sequence arising through evolutionary processes. No accounting for selection at all.

I’m guessing that the problem is more with Disqus than with your Internet. I’ve been seeing problems with Disqus for a few hours, though my Internet is otherwise fine.