Good Math/Bad Math

Sunday, April 02, 2006

One last stab at Dembski: the Vacuousness of Specified Complexity

One last stab at Dembski, and then I promise I'll move on to something else.

The thing that Dembski is most well-known for is his notion of specified complexity. The root of his anti-evolution argument is that specified complexity cannot come into being without the intervention of a conscious designer. He further claims that his notion of specified complexity is so well defined that it makes the intelligent design theory into a branch of information theory!

So first, what is specified complexity? In typical Dembski fashion, it's fairly hard to find a concise meaningful definition from him. Here's one version, from one of his many articles on the topic:

What are the candidates here for something in nature that is nonetheless beyond nature? In my view the most promising candidate is specified complexity. The term "specified complexity" has been in use for about 30 years. The first reference to it with which I'm familiar is from Leslie Orgel's 1973 book The Origins of Life where specified complexity is treated as a feature of biological systems distinct from inorganic systems. Richard Dawkins also employs the notion in The Blind Watchmaker though he doesn't use the actual term (he refers to complex systems that are independently specified). In his most recent book, The Fifth Miracle Paul Davies (p. 112) claims that life isn't mysterious because of its complexity per se but because of its "tightly specified complexity." Stuart Kauffman in his just published Investigations (October 2000) proposes a "fourth law" of thermodynamics to account for specified complexity. Specified complexity is a form of information, though one richer than Shannon information, which focuses exclusively on the complexity of information without reference to its specification. A repetitive sequence of bits is specified without being complex. A random sequence of bits is complex without being specified. A sequence of bits representing, say, a progression of prime numbers will be both complex and specified. In The Design Inference I show how inferring design is equivalent to identifying specified complexity (significantly, this means that intelligent design can be conceived as a branch of information theory).

It's longwinded, and actually quite vacuous when you actually read it carefully. But there are two notions in it: complexity, and specification. Essentially, he argues that complexity is information in the classic IT sense. Specification, he mostly waves his hands around. Let's try for some other sources to find an adequate definition.

Here's the definition from the Discovery Institute's website:

Specified complexity consists of two important components, both of which are essential for making reliable design inferences. The first component is the criterion of complexity or improbability. In order for an event to meet the standards of Dembski's theoretical notion of specified complexity, the probability of its happening must be lower than the Universal Probability Bound which Dembski sets at one chance in 10^150 possibilities.

The second component in the notion of specified complexity is the criterion of specificity. The idea behind specificity is that not only must an event be unlikely (complex), it must also conform to an independently given, detachable pattern. Specification is like drawing a target on a wall and then shooting the arrow. Without the specification criterion, we'd be shooting the arrow and then drawing the target around it after the fact.

Better than Dembski's own writing, it doesn't try to hedge around and hide behind so much verbosity. But it also reveals the essential emptiness of the argument: Specification is an a priori description of a system.

Thus, according to Dembski, you can argue that a system is designed if it exhibits two properties: (1) It is informationally complex - that is, it's structure embodies a significant amount of information; and (2) it matches an independent description of a system that performs a specific task - and that independent description must be made, independent of observations of the system in question.

So far, in terms of math, this remains a tautology: a system exhibits specified complexity if it's complex and you can describe it without looking at the system to derive the description. Remember the definition of information from Chaitin? The information contained in a system is exactly the shortest description of that system. So, so far, mathematically, the definition of "specification" has no explanatory value: every system is specified.

Ok, let's make one last try. Wikipedia's article on specified complexity gives the following definition:

In Dembski's terminology, a specified pattern is one that admits short descriptions, whereas a complex pattern is one that is unlikely to occur by chance. Dembski argues that it is impossible for specified complexity to exist in patterns displayed by configurations formed by unguided processes. Therefore, Dembski argues, the fact that specified complex patterns can be found in living things indicates some kind of guidance in their formation, which is indicative of intelligence. Dembski further argues that one can rigorously show by applying so-called no free lunch theorems the inability of evolutionary algorithms to select or generate configurations of high specified complexity. Specified complexity is also referred to by Dembski as "complex specified information" (CSI).

This is, by far, the clearest definition. Assuming Wikipedia is being fair (and the article does read as being pretty evenhanded - critical, but fair), then we finally have something meaningful.

A specified pattern is a pattern that has a short description. A complex pattern is one that is statistically unlikely. That sounds good: a system with specified complexity is a system with high complexity in the IT sense, but which has a short description.

Except - the IT definition of high complexity, which he purports to be using - says that a system is not complex if it has a short description. Which means that the definition of specified complexity is "A system which contains a lot of information, but which doesn't contain a lot of information."

Oops. No so good, eh?

The only non-vacuous explanation of SC is to discard the information theoretic part from the definition of "specification". So specification becomes "can be described simply but incompletely, in a way that is comprehensible to an intelligent observer". And the whole notion of SC becomes non-mathematical and entirely subjective - and thus useless for its purported purpose. It's a shell game.

25 Comments:

  • Might I suggest that "a system which contains a lot of information, but which doesn't contain a lot of information" applies perfectly to the kind of writing for which Dembski and his ilk are famous?

    By Blogger Thomas Winwood, at 1:25 PM  

  • While you have been writing alot about the mathematical corruption of the creationists I don't see why you have to stop. I think the creationists today are more guilty than anyone else of abusing math to advance their own agenda and they need to be exposed.

    By Anonymous CBBB, at 2:21 PM  

  • cbbb:

    I agree that the creationists are some of the most irritating math abusers out there, and I'm not permanently swearing off of smacking them down, it gets tiresome to debunk the same stupid arguments over and over. I think I've covered the basic gibberish that they like to spew, so instead of just rehashing, I'm going to look at some other purveyors of bad math. Believe me, there's no shortage of 'em/

    By Blogger MarkCC, at 2:32 PM  

  • "Oops. No so good, eh?"

    Indeed! I would go so far as to say it looks like the classic strawman.

    "Assuming Wikipedia is being fair (and the article does read as being pretty evenhanded - critical, but fair), then we finally have something meaningful".


    I disagree that "fair", whatever that means in this context, is what we should be looking for. I would think "accuracy" is what counts. We can determine that more objectively, by finding some Dembksi quote that supports said representation.

    But I don't recall Dembksi saying that "a specified pattern is one that admits short descriptions". What he has said is that a pattern is "specified if independently of the possibility's actualization, the possibility is identifiable by means of a pattern".

    Now I can't claim he never said that which is attributed to him by Wikipedia, but they certainly provide no evidence that he has.

    By Anonymous Roger R, at 3:45 PM  

  • roger r:

    I think that fairness is relevant - but fairness is not the same as "balance". A fair presentation of Dembski's ideas presents them without misrepresentation, and without interspersing insults. A fair presentation can be highly critical (and the wikipedia article is), but it does do a good job of explaining his position, even as it makes it clear how thoroughly silly it is.

    (Note that by my standards, my own posts are not particularly fair :-) )

    By Blogger MarkCC, at 5:45 PM  

  • I've looked at Dembski's writing a few times and it's typically not very concise or straightforward.
    It seems like this is part of the whole ID grand strategy. If no one knows what your arguement actually IS than if someone tries to refute it you can always just claim that they are "misrepresenting" you. This seems to be a standard ploy with IDists; Dembski's writing is generally so unclear and overly complicated that they can claim that any rebuttle is based on a strawman arguement or misrepresentation.

    By Anonymous CBBB, at 6:10 PM  

  • markcc:

    "I think that fairness is relevant - but fairness is not the same as "balance". A fair presentation of Dembski's ideas presents them without misrepresentation, and without interspersing insults."

    I won't belabor the point of how you choose to define fairness, other than to say it isn't universal. But let's return to the point you didn't adress. Does "without misrepresentation" mean "accurate"? If so, you haven't demonstrated that their claims were accurate. Indeed, you just seemed to assume "fairness", and hence accuracy. But I want to see some evidence that what they claimed is Dembski's position, really is.

    That would seem to be the key to whether it was "fair" or "without misrepresentation" or "evenhanded". I don't see how you can conclude all those positions without evidence.

    By Anonymous Roger R, at 6:50 PM  

  • But I don't recall Dembksi saying that "a specified pattern is one that admits short descriptions".

    Take a look at section 4: Specifications via Compressibility.

    By Anonymous MartinM, at 7:00 PM  

  • rogerr:

    The reason that I asserted that wikipedia's entry about Dembski was fair is because, based on my readings of Dembski, that their article does accurately represent what Dembski says.

    Dembski is a very wordy, obfuscatory writer; I don't think he'd ever say anything in as few words as the definition I took from wikipedia. But from reading his various writings, it does seem like that wikipedia definition is what "specification" means to him; for all of his wordiness, he stresses things like "patterns", conciseness, simplicity, clarity, etc.; the examples that he cites are always ones where the "specification" is a simple description.

    So I conclude that it *is* a valid definition of his term. And I further conclude that he is deliberately obfuscatory, because he knows that he's formulating something which is mathematically gibberish, but which has an intuitive appeal, and which can be connected to mathematics in way which makes it look like more than it actually is.

    What I find particularly interesting about Dembski's writing is that he sometimes uses math in his descriptions/definitions of "complexity"; but his descriptions/definitions of specification don't.

    By Blogger MarkCC, at 7:12 PM  

  • I'm not sure you've got the definition of SC right here. It's significant that it combines the two different types of "information" - improbability (a la Shannon) and complexity.

    If I understand it correctly (which is unlikely but hey), the idea is that improbable specified results don't come about through chance, and that complex specified results don't come about through natural causes. This is complete bull as far as I can tell, but it's actually quite good bull in that it sidesteps many of the classic counterexamples. For example, a snowflake would be complex but not specified. A DNA strand, on the other hand, would be improbable, complex and (by the fact that it presumably does something interesting) specified.

    The definitions Dembski uses (especially of specification) are horribly sloppy, and the proofs are a mess, and of course it all falls down when you throw genetic algorithms into the mix. I've gotta say, though, that SC is about what I think I'd have come up with if I were trying to eliminate natural causes as an option. It's badly wrong and certainly doesn't deserve to be considered mathematics, but otherwise it's quite a cute concept.

    By Blogger Lifewish, at 7:19 PM  

  • Oh, by the way, is it just me or does "X is specified" basically mean "X looks cool"?

    By Blogger Lifewish, at 7:20 PM  

  • "Take a look at section 4: Specifications via Compressibility. "

    I looked at it. Didn't see anything like it there.

    By Anonymous Roger R, at 7:51 PM  

  • "The reason that I asserted that wikipedia's entry about Dembski was fair is because, based on my readings of Dembski, that their article does accurately represent what Dembski says."


    Then by all means, provide me with a citation of Dembski saying it in 500 words, or an entire chapter, or whatever. Because I don't remember ever seeing that in my Dembski readings. And I'm guessing that I've probably read more of him than you, if this comment is any indication:

    "What I find particularly interesting about Dembski's writing is that he sometimes uses math in his descriptions/definitions of "complexity"; but his descriptions/definitions of specification don't. "


    It logically follows from how he defines the two concepts. Nothing suspicious about that. Specification is not easily quantifiable, any more than Natural Selection is. One can certainly question the concept of specification, as David Berlinksi of the Discovery Institute does, but then one has to live within the constraints of said criticism.

    You seem to want to say two different things: that Dembski is writing a lot and saying nothing of significance, and that what he says is significant, but incorrect. Those positions are not easily reconcilable.

    By Anonymous Roger R, at 8:07 PM  

  • Well like I said Roger r is playing the old creationist shell game perfectly.
    Keep the definitions and concepts vague so that when challenged you can just scream about how you're unfairly being "misrepresented".

    By Anonymous CBBB, at 8:16 PM  

  • And cbbb, your comments capture pretty succinctly why I am no longer a Darwinian, but a Darwinian critic.

    As Scott Adams said, "The people who purport to have evidence of evolution do a spectacular job of making themselves non-credible."

    By Anonymous Roger R, at 8:35 PM  

  • Scott Adams eh? Taking science advice from a cartoonist?
    So let me get this straight you don't really care about facts or evidence so much as you just like to be on the side with the "nicer people" - is that it?

    Well I have to say time and time again I see IDist accusing critics of mispresenting thier position but they never seem to make their position quite clear. All I can say is any mispresentations are their fault because I can't find a nice concise definition of Dembski's apparently "well-defined" and "widely accepted" concepts.

    By Anonymous CBBB, at 8:48 PM  

  • roger:

    Fine, if you believe that I've misrepresented Dembski, then how about you give me a concise, mathematical definition of what it is that Dembski is talking about when he says "specification".

    Using the quote you provided earlier: "specified if independently of the possibility's actualization, the possibility is identifiable by means of a pattern", what does it mean?

    There's two bits of content in there. The first is "independent of the possibility's actualization"; that is, the "specification" is independent of the actual real incarnation of the specification; and "identifiable by means of a pattern". What does it mean to be identifiable by a pattern? Well, Dembski claims to be talking about information theory; in IT, a pattern is a redundancy which allows the information to represented in a concise form.

    And according to Dembski, specification must be quantifiable: he's arguing that the concept of specified complexity is an extension to algorithmic information theory (aka Kolmogorov complexity); AIT is the mathematics of quantifying information. If he wants to claim that he's using AIT to argue for the impossibility of specified complexity occuring naturally, then he must provide a specific, mathematical, quantifiable definition of specification. But at doing that, he fails utterly: he buries it under mounds of argument, without ever actually saying what it is. And it's my opinion that that's deliberate: he's too good a mathematician to be doing this by accident.

    And what I'm saying about Dembski is not contradictory. What I'm saying is that he uses a gloss of mathematics to make it appear that he's saying something with significant depth and mathematical support; while in fact, his math is at best sloppy, and utterly irrelevant to the argument he's making: from a mathematical viewpoint, he's completely vacuous; his mathematical arguments do not mean what he says they mean.

    By Blogger MarkCC, at 9:08 PM  

  • In your first quote from Dembski, there is this:

    "A sequence of bits representing, say, a progression of prime numbers will be both complex and specified."

    Would it be worthwhile to run through what the computational content of such a sequence is? It seems like he is trying to get his mileage out of things that we think we have an intuitive feel for but that few of us can process formally. If he has a few other examples besides just the primes, maybe looking at the cases would help show what his gig is.

    By Blogger driftwood, at 11:45 PM  

  • You know Mathematician Jeffery Shallit and Biologist Wesley Elsberry wrote a good paper on Dembski's "math" a few years ago:

    http://www.antievolution.org/people/wre/papers/eandsdembski.pdf

    Worth reading I think, of course true to form the creationists have accussed them of misrepresenting their position.

    By Anonymous CBBB, at 12:05 AM  

  • CSI is supposed to be the criterion for design. As you pointed out, Specification has not been unambiguously specified. In addition to what you wrote, Dembski sycophant Salvador Cordova has said a few times that something is specified if it corresponds to a platonic ideal. Which is a useless thing to say. But of course the IDers never really use CSI to detect design, they use, "Don't that look designed? I guess it was." as you can see all over the internet:

    http://www.uncommondescent.com/index.php/archives/988

    By Anonymous Anonymous, at 4:56 PM  

  • roger r, if you would read the paper that martinm cited, you would see that Dembski's latest incarnation of specified complexity is inversely proportional to the length of the event's description (see the bacterial flagellum example). So, yes, specification explicitly denotes short descriptions.

    The problem is that the universal distribution (see here) observes that simple deterministic processes are common, so short descriptions (low Kolmogorov complexity) would indicate a deterministic process, which, according to Dembski, cannot generate SC.

    By Anonymous secondclass, at 7:22 PM  

  • OK, this is pretty back-of-the-envelope, but what are the odds of a particular snowflake? How does it fit into "specified complexity"?

    Assuming we need to create a six-sided figure with absolute symmetry, and starting with a smaller snowflake of n molecules, we can figure the odds of getting another snowflake with n+12 sides (use 12 instead of 6 because each arm has bilateral symmetry). The first molecule can attach anywhere, but the next one has to go in one of the 11 symmetric slots, etc., until we have generated another symmetric snowflake. Thus, PsubN is (12/12)(11/12)(10/12)...(2/12)(1/12) Psub(N-12). If a snowflake has about 10^20 molecules, that says that the probability of generating a fully symmetric snowflake is on the order of 10^.35(10^20).

    Sure, I made some simplifying assumptions, but I don't think they ruin the result that this is horribly larger than Dembski's 10^150.

    Clearly, snowflakes must be designed. Each one. Individually.

    By Anonymous Ahcuah, at 12:47 AM  

  • Sure, I made some simplifying assumptions, but I don't think they ruin the result that this is horribly larger than Dembski's 10^150.

    Clearly, snowflakes must be designed. Each one. Individually.


    That's where the specification bit comes in. It's only specified (Dembski uses the phrase "detached specification") if, in some sense, you could have come up with a descriptor for it beforehand. There's at least three valid objections to this concept*, but the snowflake isn't one of them. That's what I meant about SC sidestepping most of the obvious counterexamples.

    * 1) it's horribly subjective

    2) I would disagree that the specifications suggested for stuff like flagella are in any way detached.

    3) this only works if there's no natural tendency for objects of a given type to converge to a specific pattern. For example, if you were looking at the pattern of puddles formed by heavy rain, the specification "the pattern of puddles that formed last time we had this much rain" wouldn't work.

    By Blogger Lifewish, at 7:18 AM  

  • How about the specification, "grilled cheese sandwiches that look like Jesus"?

    By Anonymous bmurray, at 8:08 AM  

  • (1)The three definitions attributed to D. seem to be definitions of quite different items (where they are sufficiently clear to define anything at all), and two of them seem logically opposed, i.e., the two definiens couldn't apply to one and the same definiendum.

    (2) With regard to roger r's quote from D., it seems to me that all the possible outcomes -- no matter how short or long their description -- of any set whose elements are capable of chance arrangements can, in principle, be described in advance. (Issues with uncountable sets seem to be irrelevant.)

    (3)A problem with shutting the door on ID too firmly is that one might close off any solution to the prob- lem of other minds. (I know I am conscious because I am immediately aware of my thoughts and feelings. But I am not inside your head: I must infer your conciousness from what I hear you say and see you do.) This, of course, is the Turning test, and passing or probably pass- ing the Turing test is surely a mat- ter of inductive inference from ob- servable patterns of behavior. The possible difficulty is obvious.

    gph

    By Blogger Greg P. Hodes, Ph.D., at 3:11 AM  

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