Good Math, Bad Math

While perusing my sitemeter stats for the page, I noticed that I’d been linked to in a discussion at creationtalk.com. Expecting amusement, I wandered on over to see who was linking to me.

Someone linked to my index of articles debunking Dembski and Berlinski. The moderator of the creationtalk forum responded to my series of articles on information theory and Dembski with:

No offense to you or him, but his arguments kind of suck. I looked at his response to Behe on IC, and Dembski on Specified Complexity , to Behe’s he didn’t refute it, and to Dembski’s his only arguement was basically summed up to “I don’t know the definition of specified complexity oh mercy”.

For readers who remember, my critique of Behe was that the entire concept of “irreducible complexity” is mathematically meaningless. It’s true that I didn’t refute Behe, in the sense that I didn’t waste any time arguing about whether or not irreducible complexity is indicative of design: there’s no point arguing about the implications of an irreducibly complex system if, in fact, we can never recognize whether a system is irreducibly complex. Sort of like arguing about how many steps it takes to square a circle, after you’ve seen the proof that it can’t be done in a finite number of steps.

But the Dembski line is the one that’s particularly funny. Because, you see, my critique of “specified complexity” was that you can’t mathematically refute specified complexity because Dembski never defines it. In paper after paper, he uses obfuscatory presentations of information theory to define complexity, and then handwaves his way past “specification”. The reason for this is that “specification” is a meaningless term. He can’t define it: because if he did, the vacuity of the entire concept becomes obvious.

A complex system is one which contains a lot of information; which, in information theory, means a system which can’t be described with a brief description. But specification, intuitively, means “can be described concisely”. So you wind up with two possibilities:

  1. “Specification” has a mathematical meaning, which is the opposite of “complexity”, and so
    “specified complexity” is a contradiction; or

  2. “Specification” is mathematically meaningless, in which case “specified complexity” is a meaningless concept in information theory.

The problem isn’t that “I don’t know the definition of specified complexity”. It’s not even that there is no definition of specified complexity. It’s that there cannot be a definition of specified complexity.

I’ll probably drag out my original Dembski and Berlinski tomorrow, polish them up a bit, and repost them here at ScienceBlogs.

Comments

  1. #1 bigdumbchimp
    June 13, 2006

    obfuscatory presentations of information theory

    I think this must be listed in the secret ID handbook as one of their top tactics.

    I also like to refer to these similar types of long drawn out “arguments” full of impressive words and phrases with complex but meaningless explanations as “Techno Filibusters”. I have to deal with them frequently from vendors trying to sell me on their newest IT technology that can’t really stand up to the competition.

  2. #2 Dave S.
    June 13, 2006

    The main strength of specified complexity is that its so vague it can be used to infer ‘design’ pretty much at will. In most any real world situation the calculations necessary to determine complexity cannot be performed since we lack the necessary information. Specificity isn’t defined in any consistent way, and in practice is always determined post hoc, which allows anyone so inclined to proclaim anything they choose to be specified. Its merely a fancy way of saying something is designed because gee it sure looks designed.

  3. #3 Mark C. Chu-Carroll
    June 13, 2006

    Dave:

    Yup, you nailed it right on the head. That’s exactly what I was trying to point out in my original critique. It’s a deliberately undefined term, and a deliberately unverifiable property. It allows creationists to gives a non-falsifiable appearance of science to a bunch of bogus claims, while keeping a convenient out – anytime they’re shown to be wrong about some system they babbled about, they can just say “but it wasn’t specified”.

  4. #4 Dave S.
    June 13, 2006

    I’ll have to check out the original critique Mark.

    No doubt you are already familiar, but I’m reminded of a famous (and possibly somewhat apocryphal as these things are) story about the British mathematician G.H. Hardy, who when visiting his friend Srinivasa Ramanujan in the hospital happened to mention that the number of the cab that had brought him there was 1729, and that that number was rather uninteresing and not at all special. Ramanujan admonished him that it was in fact a very intriging number, as it was the smallest number expressible as the sum of two positive cubes in two different ways.

    The point being that pretty much any number, and by extension IMO any pattern, could be seen as “special”, or specified, in some way. It just depends on the observers say so.

  5. #5 secondclass
    June 13, 2006

    If you query three IDists, you’ll get four different definitions of specified complexity. If you query Dembski, you’ll get five.

  6. #6 Davis
    June 13, 2006

    The point being that pretty much any number, and by extension IMO any pattern, could be seen as “special”, or specified, in some way. It just depends on the observers say so.

    Classic proof that all (whole) numbers are interesting: suppose not. Then there must exist a smallest uninteresting number, which is interesting by virtue of the fact that it’s the smallest uninteresting number. Contradiction.

    The funny part is, that proof is less vacuous than the IDists’ “math.”

  7. #7 Mark C. Chu-Carroll
    June 13, 2006

    Davis:

    Interestingly, you’re actually right on top of something that Greg Chaitin, one of the geniuses of information theory, is fascinated by.

    One of the things Greg has written a lot about is strange self-referential numbers. One of the easiest ways to define one of those strange numbers is exactly what you said.

  8. #8 Davis
    June 14, 2006

    One of the easiest ways to define one of those strange numbers is exactly what you said.

    By that you mean replace “interesting” with “self-referential”?

    This sounds neat — I’ll have to take a look at Chaitin’s work (once I finish revising my thesis, that is).

  9. #9 Daniel Morgan
    August 24, 2006

    Mark,

    For whatever reason, I somehow missed this post. Skiddum on the cretalk board (and the Darwintalk.com board) is me. I responded to Tim, the moderator you refer to, with this post, and he basically didn’t even try to explain how you failed to refute entirely Dembski’s work.

    Anyway, keep up the good work!

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