Good Math/Bad Math

Tuesday, April 25, 2006

Dembski and Displacement

I've been requested to comment on a relatively recent paper by Dembski,
Searching Large Spaces : Displacement and the No Free Lunch Regress, in which he essentially attempts to use his "No Free Lunch" theorem to show that something like evolution requires an intelligent guide.

Frankly, I'm pretty tired of talking about Dembski; but I think this paper is interesting in a few ways: it's blatantly dishonest in a way that's unusual even for Dembski; it demonstrates some classic creationist misdirections; and it demonstrates what the ultimate point of NFL is for Dembski.

The Blatant Dishonesty: Uniformity

As usual, Dembski is using his No Free Lunch (NFL) theorems as a way of arguing that evolution couldn't possibly have produced life as it exists on earth. But it's got the same problem as all of this other NFL stuff; in fact, it's got the same problem in an even more extreme form. Dembski's argument models evolution as a search function; and it treats the search space as perfectly uniform.

Yeah, if you've got a perfectly uniform search space, and you want to search it with a fixed search function, then guess what: the probability of your search finding its target is damn poor. Yippee. Not exactly a profound statement.

The "novelty" of this paper is that it also considers various kinds of meta-searches: that is, searches where instead of just choosing a search function, you use a search to find a search function well-suited to the search space.

Guess what? If you've got a uniform search space, then searching for a good search function that can find the target doesn't work well: the probability of finding a search function that will find the target even lower than the probability of a random search function finding the target. Going blindly meta on the search isn't better than just doing a blind search; in fact, it's worse.

This is not a profound result.

But the real problem here, the real fundamental dishonesty, is that Dembski continues to use a deliberately ridiculous model - one whose errors have been pointed out to him numerous times, and which he continues to ignore. He models evolution as a search for a specific target in a uniform search space using a single fixed search function. His concession to the criticisms of this model is to allow the search function to be stochastic - which is really no concession at all. (A stochastic search function doesn't pick a direction for the next step of the search; it assigns probabilities to the various directions that you could progress in, where the probabilities are its guesses about how likely you are to find the target in that direction.

Evolution is not a search using a fixed search function over an arbitrary uniform space. The search space is not uniform; the "search function" is not fixed; there is no specific target. It's the same old nonsense: if you create a model of the evolutionary process which eliminates the properties that make evolution work, then you can use that model to show that evolution doesn't work.

Dembski even pulls out that favorite creationist canard: the old "probability of a protein 100 amino acids in length". Dembski knows full well that this is garbage - it's been pointed out to him numerous times. But he doesn't let that stop him - and it's a perfect demonstration of exactly what's wrong with his entire argument:
Take the search for a very modest protein, one that is, say, 100 amino acids in length (most proteins are at least 250 to 300 amino acids in length). The space of all possible protein sequences that are 100 amino acids in length has size 20^100, or approximately 1.27x10^130.
No process in evolution searches for a specific protein. Not every chain of amino acids is even possible. The "probability space" of protein chains is very non-uniform: because of geometric constraints, some chains are very likely; some are very unlikely; and some are impossible. So if you want to model a search for a protein, the search space is not a search for 1 in 20^100; it's a search for some protein which is suited to some purpose (which is likely a family of similar proteins) in a non-uniform search space in which some things are far more likely to appear than others.

This is exactly the problem with all of Dembski's NFL arguments: the insistence for uniform search spaces; the insistence on a single fixed target; and the insistence on a single fixed search function.


The fundamental point of this paper is to try to turn NFL into some kind of support for intelligent design: it wants to argue that blind searches can't work, and that directed searches can work, but only if they have intelligent guidance.

It's a total misdirection. He's structured things so that no search can work unless you know how to get to the target in advance, and then argues that you can't get to the target unless you know it in advance. Phrased in simple english, this is incredibly obvious. But Dembski plays the standard trick of creationists: dazzle you with so much verbose nonsense and impressive-looking math that the tautological nature of the basic argument is hidden.

Here's an example:

What the heck does this mess say? If you used a meta-search to add information to a search function, then you used a meta-search to add information to a search function.

The Point: Dembski's Agenda

This paper is by far the clearest demonstration of exactly what the point of all of Dembski's NFL stuff is about. Dembski wants to argue for intelligent design. He's trying to create a mathematical argument for why there must be an intelligent guide for evolution to work. His agenda for this is to argue that first, there's no way that simple unguided evolution can possibly work. That's the basic NFL stuff. This paper augments that: it tries to show that it can work if the process is guided - but only if the guide has the property that its guidance adds information to a search through its guidance; and finally, he wants to argue that no random process can create a "guide" for search that adds information - the guide must be an intelligent being.

It's intelligent design expressed through mathematical misdirection. By carefully structuring things, and throwing lots of math around, he builds the assumption that an intelligent designer is needed into his framework, and then uses that framework to show that an intelligent designer is needed.


  • Every time I look at something of Dembski's, I get that same feeling. It's like he's playing 10^18 (or maybe 10^12) card Monty.

    The point isn't how many cards he uses. The point is that he's cheating.

    N card Monty isn't a card game; it's a hustle.

    By Anonymous Jim Ramsey, at 12:40 PM  

  • Dembski's argument perfectly illustrates my now-favorite distinction between "Theological Arguments" and "Scientific Arguments"

    "Theological Arguments" pre-suppose the conclusion: e.g. "God is All-Present". They then search the world for examples to support the conclusion. Anything "facts" that don't fit must be rejected or re-worked until they do fit. Indeed, they aren't "facts" until they are made to fit the conclusion!

    "Scientific Arguments" start from the facts of the world, and look for structures (called "theories") to organize them.. Any "theories" that don't fit must be rejected or re-worked until the do fit. Indeed, they aren't "theories" until they are made to fit the facts!

    Tracy Hall

    By Anonymous Tracy Hall, at 2:27 PM  

  • Ewwww. It's as if the Brothers Bogdanov decided to take up the fight for creationism. Nasty, nasty math.

    By Blogger Blake Stacey, at 2:40 PM  

  • I term Dembski's god as the informational god, a god who 'breethes' information into the world. I always find it interesting and perculiar. Given that God is supposed to be omniscient, one would expect he would inject pure 'information' into this world. For anything less would be inefficient. And an inefficient god would not be omnipotent, another one of those 'godly' attributes. But since neither pure 'random' strings and pure 'informational' is compressible, they are for all pratical purposes indistinguishable. So a informational god that intervene in this universe is indistinguishable from pure randomness.

    By Blogger RandomDNA, at 9:58 PM  

  • I wonder, isn't the mere existence of working evolutionary algorithms a trivial counterexample against Dembski's "proof"?

    By Anonymous Anonymous, at 1:34 AM  

  • Anonymous:

    I agree with you that evolutionary algorithms are a counterexample to Dembski; but he argues that the implementation of the evolutionary framework that we use to run ev algorithms is "adding information" that allows the system to work in a way that an unguided system can't. Even when the randomness of those systems is pointed out to him, he insists that the human-designed framework is implicitly injecting information, even if it isn't deliberate.

    In fact, he goes so far as to argue that his NFL stuff *proves* that evolutionary algorithms can't work unless we're somehow injecting information.

    By Blogger MarkCC, at 8:06 AM  

  • Another of your many good anti-ID entries.

    Pointed people over to your blog, by the way.

    By Blogger Bronze Dog, at 9:14 AM  

  • Pointed people over to your blog, by the way.

    And I took the bait.

    Great post. I'll be returning frequently.

    By Blogger Rev. BigDumbChimp, at 6:34 PM  

  • Hi MarkCC:

    I agree with much of your Blog about Dembski. Please consider this what if scenario.

    What if he and Behe had instead argued that nucleic acids [DNA, RNA] may be an irreducible complexity? [instead of their ridiculous flagella and clotting examples.]

    These information storage and retrieval helicoids [genus?] can also manufacture themselves, proteins, carbohydrates and lipids that allow for reproduction and adaptation of various life forms to various environments.

    Nucleic acids seem to use a nested binary ‘this or that’ code [DNA or RNA, purine or pyrimidine, A or G., C or (T or U)] with T specific for DNA and U specific for RNA.

    Nucleic acids also have an ionic charge for various bonding properties. I am relatively certain they are harmonic oscillators. I speculate they may have an imaginary unit component because of the ionic charges.

    One can almost think of them playing the song of life.

    Dembski and Behe may have inadvertently supported evolution theory in this scenario.

    If any of this is so, nucleic acids may have a lot in common with music theory which is also an informational system. [Please consider more matrix information in a future blog as I tend to find waves easier to understand.]

    Steinmetz EE phasor equations [based on Grassmann Algebra] and Schroedinger QM wave mechanics are helical 3D structures that allow for predictable results. They appear to have informational properties. [I speculate that Schroedinger knew music theory and Heisenberg did not. This may be why Heisenberg had difficulty accepting wave-matrix equivalence or duality. I have not been able to find ant information regarding their musical hobbies.]

    Planetary orbits like that of Earth are traditionally described as a nearly circular ellipse. This is true only when the sun is motionless. With the sun in motion, the Earth orbit becomes a helix [Earth-Moon a double helix] which seems to be the case for most celestial mechanics .

    I speculate that vibrating strings and even QLG may also be harmonic oscillators.

    The helix and helicoid appear to have astonsihing importance with a nesting [or embedding] through many different physical gauges, almost all capable of conveying some type of information.

    They also have permutation and symmetry.

    By Anonymous Doug, at 6:43 PM  

  • [Re: the bit about information functions and indicator functions and so forth]
    What the heck does this mess say?

    You know the great thing about that mess in particular? He's saying, in as obfuscatorily set-theoretic language as possible, that his definition of "assisted search" requires each single response of the assistant to, at minimum, tell you whether you're on top of the target or not.

    The wonderful thing is that a page or so earlier his "prototypical example" for an assisted search is an Easter Egg hunt, where the assistant says "warmer" or "cooler" as you move around. "Warmer," of course, does not tell you whether you've reached the target. It just tells you you're going in te right direction.

    So that section isn't just shallow and impenetrably written, it's blatantly self-contradictory. Hilarious.

    By Anonymous Anton Mates, at 9:06 PM  

  • It's really too bad that evolution is seen in such a bad light because of Dembski and the like. I've always thought that the critics of evolution would be quiet if the theory became formalized. This being a math blog, I was wondering if anyone has any opinions on this matter. I'm a biologist and wish desperately for a good mathematical definition. Perhaps we could start calling it the law of evolution...

    By Anonymous Lance Pickens, at 11:47 AM  

  • Lance: problem is that afaict evolution basically boils down to "stuff changes and sucky stuff doesn't reproduce". That's not something that's easy to formalise.

    For bonus points, the space of possible genomes is infinite-dimensional, the map from genomes to phenomes is badly-behaved as only biology can be, and the fitness function literally changes as the weather does. The genetic algorithm we're part of is mathematically disgusting.

    Possibly you could come up with something that would be to genetic algorithms as economics is to game theory - I'll give it some thought.

    By Blogger Lifewish, at 12:17 PM  

  • Lance, the critics of evolution will never be quiet. They don't care whether evolution is true or not. They care whether you believe it or not, and whether you believe their brand of theism.

    Demsbki isn't putting this stuff out to persuade mathematicians and biologists. It's for people who won't understand a bit of it, but want to be reassured that ID is "scientific." They won't understand (or believe) the refutations, either.

    So, no, they'll never shut up. Sorry.

    By Anonymous S Hanley, at 8:41 AM  

  • Hey can you address this? I came up with it totally without input from Dembski. . . .

    In Him,

    David S. MacMillan III

    By Blogger David S. MacMillan III, at 6:14 PM  

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