Monday, January 09, 2006

William Dembski....can he add up etc.

I brought this up before but I noticed someone who left a comment to the effect that Dembski's mathematical abilities are under question. I have heard contradictory views about this and I am personally not in a position to give his mathematical work a careful scrutiny... I am however very interested. I have heard it suggested that the inventor of the "No free lunch theorems" thinks that he abused them and I have heard that Dembski and Shallit are not on speaking terms for one reason or another. I have also heard that his maths is fine from other people is just he muddles up the conclusions!

It surely shouldn't be difficult for someone who is well qualified to work out whether he is competent and whether his work is leading to valid conclusions or not.

Who am I supposed to believe on this and why?
Can someone qualified and respected give me a truly objective report on Dembski's mathematical ability? Did CUP make a big error or not?


Blogger Lifewish said...

I'll get on it now*. I'm still only a third-year uni student, but I've taken the relevant courses and from what I've seen it's not rocket science. I don't have Dembski's book, but the pdf of his paper on his Displacement Theorem is floating around online so I'll have a go at that.

* For "now" read "when I've finished Quantum Mechanics"

2:46 pm  
Anonymous Anonymous said...

For an interesting comment on Dembski's abilities as a mathematician this is a good read from the Dover trial archive on NCSE; (shallit.pdf)

Shallit would have been a rebuttal witness for the plaintiffs had Dembski been allowed to testify.

9:34 pm  
Blogger Lifewish said...

OK, I finally got round to dissecting Dembski's paper. It wasn't easy - he has a fairly... eclectic style.

Turns out* that there is indeed a big hole in his approach. He's completely ignored the possibility that the algorithm's behaviour and the target space are fundamentally interdependent, and is thus concluding that the fact that they overlap is too implausible to be explained by chance. This is like saying that it's a miracle that water stays in seas rather than flowing all over the mountaintops.

Given that this interplay between target space (or rather fitness function) and algorithm is the entire damn point of genetic algorithms, this is (if accurate) a fairly lame mistake to make. I'll hopefully sort out a full mathematical exposition at some point to ensure that what I'm saying here is rigorous.

1) I'm only a maths student, not even got my BA yet. So it is quite possible that I've got something wrong. I don't think I have though.
2) I need to read the paper a couple more times to make absolutely sure I've got it right. The above conclusion is provisional.

6:32 pm  

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