Dembski and No Free Lunch with Competitive Agents (updated repost from blogger)

Jun 14 2006 Published by under Debunking Creationism

(Continuing in my series of updates of the GM/BM posts about the bad math of the IDists, I'm posting an update of my original critique of Dembski and his No Free Lunch nonsense. This post has more substantial changes than my last repost; based on the large numbers of comments I've gotten in the months since then, I'm addressing a bit more of the basics of how Dembski abuses NFL.)

It's time to take a look at one of the most obnoxious duplicitous promoters of Bad Math, William Dembski. I have a deep revulsion for this character, because he's actually a decent mathematician, but he's devoted his skills to creating convincing mathematical arguments based on invalid premises. But he's careful: he does his meticulous best to hide his assumptions under a flurry of mathematical jargon.

One of Dembski's favorite arguments is based on the no free lunch theorems. In simple language, the NFL theorems say "Averaged over all fitness landscapes, no search function can perform better than a random walk".

Let's take a moment to consider what Dembski says NFL means when applied to evolution.

In Dembski's framework, evolution is treated as a search algorithm. The search space is a graph. (This is graph in the discrete mathematics sense: a set of discrete nodes, with a finite number of edges to other nodes.) The nodes of the graph in this search space are outcomes of the search process at particular points in time; the edges exiting a node correspond to the possible changes that could be made to that node to produce a different outcome. To model the quality of a nodes outcome, we apply a fitness function, which produces a numeric value describing the fitness (quality) of the node.

The evolutionary search starts at some arbitrary node. It proceeds by looking at the edges exiting that node, and computes the fitness of their targets. Whichever edge produces the best result is selected, and the search algorithm progresses to that node, and then repeats the process.

How do you test how well a search process works? You select a fitness function which describes the desired outcome, and see how well the search process matches your assigned fitness. The quality of your search process is defined by the limit of the following:

  1. For all possible starting points in the graph:
    1. Run your search using your fitness metric for maxlength steps to reach an end point.
    2. Using the desired outcome fitness, compute the fitness of
      the end point

    3. Compute the ratio of your outcome to the the maximum result
      the desired outcome. This is the quality of your search for this length

So - what does NFL really say?

"Averaged over all fitness functions": take every possible assignment of fitness values to nodes. For each one, compute the quality of its result. Take the average of the overall quality. This is the quality of the directed, or evolutionary, search.

"blind search": blind search means instead of using a fitness function, at each step just pick an edge to traverse randomly.

So - NFL says that if you consider every possible assignment of fitness functions, you get the same result as if you didn't use a fitness function at all.

At heart, this is a fancy tautology. The key is that "averaged over all fitness functions" bit. If you average over all fitness functions, then every node has the same fitness. So, in other words, if you consider a search in which you can't tell the difference between different nodes, and a search in which you don't look at the difference between different nodes, then you'll get equivalently bad results.

Ok. So, let's look at how Dembski responds to critiques of his NFL work. I'm going to focus on his paper Fitness Among Competitive Agents.

Now, in this paper, he's responding to the idea that if you limit yourself to competitive fitness functions (loosely defined, that is, fitness functions where the majority of times that you compare two edges from a node, the target you select will be the one that is better according to the desired fitness function), then the result of running the search will, on average, be better than a random traversal.

Dembski's response to this is to go into a long discussion of pairwise competitive functions. His focus is on the fact that a pairwise fitness function is not necessarily transitive. In his words (from page 2 of the PDF):

From the symmetry properties of this matrix, it is evident that just because one item happens to be pairwise superior to another does not mean that it is globally superior to the other. But that's precisely the challenge of assigning fitness of competitive agents inasmuch as fitness is a global measure of adaptedness to an environment.

To provide such a global measure of adaptedness and thereby to overcome the intransitivities inherent in pairwise comparisons, fitness in competitive environments needs therefore to factor in average performance of agents as they compete across the board with other agents.

To translate that out of Dembski-speak: in pairwise competition, if A is better than B, and B is better than C, that doesn't mean A is better than C. So, what you need to do to measure competitive fitness, you need to average the performance of your competitive agents over all possible competitions.

The example he uses for this is a chess tournament: if you create a fitness function for chess players from the results of a serious of tournaments, you can wind up with results like player A can consistently beat player B; B can consistently beat C, and C can consistently beat A.

That's true. Competitive fitness functions can have that property. But it doesn't actually matter: because that's not what's happening in an evolutionary process. He's pulling the same old trick that he played in the non-competitive case: he's averaging out the differences. In a given situation, a competitor does not have to beat every possible other fitness function. It does not have to be the best possible competitor in every possible situation. It just has to be good enough.

And to make matters worse for Dembski, in an evolutionary process, you aren't limited to picking one "best" path. Evolution allows you to explore many paths at once, and the ones that meet the "good enough" criteria will survive. That's what speciation is. In one situation, A is better, so it "wins". Starting from the same point, but in a slightly different environment, B is better, so it wins. Both A and B win.

You're still selecting a better result. The fact that you can't always select one as best doesn't matter. And it doesn't change the fundamental outcome, which Dembski doesn't really address, that in an evolutionary landscape, competitive fitness functions do produce a better result that random walks.

In my taxonomy of statistical errors, this is basically modifying the search space: he's essentially arguing for properties of the search space that eliminate any advantage that can be gained by the nature of the evolutionary search algorithm. But his only argument for making those modifications have nothing to do with evolution: he's carefully picking search spaces that have the properties he wants, even though they have fundamentally different properties from evolution.

It's all hidden behind a lot of low-budget equations which are used to obfuscate things. (In "A Brief History of Time", Steven Hawking said that his publisher told him that each equation in the book would cut the readership in half. Dembski appears to have taken that idea to heart, and throws in equations even when they aren't needed, in order to try to prevent people from actually reading through the details of the paper where this error is hidden.)

25 responses so far

  • Dave S. says:

    Mark writes:

    In a given situation, a competitor does not have to beat every possible other fitness function. It does not have to be the best possible competitor in every possible situation. It just has to be good enough.

    Or in chess terms - you don't have to win every game against every opponent to win the tournament, you just have to get more points in total than anyone else.

  • Rich says:

    Dave,
    My reaction to your comment reminds me of a common perception of people -- that somehow evolution (or ID) arrives at the overall winner. You still seem to be looking for the winner of the chess tournament.
    As far as I can see, evolution is more like the story of the group of hikers who talk about what they'll do if they run into a bear: "But I don't have to run faster than the bear -- I just have to run faster than you".
    IMHO... I don't see how evolution is restricted to finding 'optimums' -- it is just looking for survivors.
    Rich C.

  • secondclass says:

    A little off topic:
    To witness new depths of NFL-based obfuscation*, read this. Dembski takes a convoluted path through a simple concept, adding to the confusion by overloading terms, and tops it all off with a non sequitur.
    Dembski is under the impression that anything that isn't completely random must be the product of intelligent selection. This includes the laws of physics. After all, if you randomly pick a universe out of an equiprobable distribution of all conceivable universes, it's very unlikely that the selected universe will have simple, predictable physical laws.
    But who says that our universe was randomly picked out of such a distribution? Dembski is making unwarranted assumptions about ultimate causes and the fundamental nature of reality. Maybe reality is fundamentally regular, and randomness is the exception.
    * Dembski once made the following claim: Indeed, most people who comment on my writing, fans and even some foes, think that I'm an exceptionally clear writer.
    Articulate? Yes. Clear? No way.

  • Anonymous says:

    Even Tegmarks classes of multiversas are ruled by laws. But that doesn't really matter. That we see order is an anthropic bias. And there are several reasons to expect ordered universas or parts of them.
    What Dembski relies on is a Conservation of Information Theorem that as all his other concepts is wrong. (He must be breaking the second law of thermodynamics, so he places himself with the perpetuum mobile of the second kind crackpot crowd.) The only special case of conservation of information we reliable observe is in the creationist universe - the information content stays at zero.

  • Pi Gu says:

    So, essentially, evolution is not a zero-sum game. There can be more than one winner and more than one way to win. (Maybe instead of saying "winner" I should say "successful new species".)
    Do I have it correct or is there more to it than that?

  • Christian Albert says:

    "After all, if you randomly pick a universe out of an equiprobable distribution of all conceivable universes, it's very unlikely that the selected universe will have simple, predictable physical laws."
    reminds me Feynman illustrating this logical fallacy by feining astonishment at seeing a specific licence plate

  • Pi:
    Yup, you got it exactly.

  • skye says:

    You dont need good math to debunk Atheistic Evolution. And This is where Dembski goes wrong he plays ball with Atheists and Evolutionists when he doesnt need to.
    There is a simple truth and I am quite sure you will insult it with some heavy pseudo-intellectual gymnastics.
    Without intelligence as a source and basis for knowledge and Intelligence, then both those words have no meaning and no purpose. Hence any argument for Atheistic Evolution is useless.

  • skye:
    You don't need any kind of gymnastics to debunk the stupidity of a statement like that. It's a meaningless, circular statement.
    Just replace "intelligence" with "X":
    "Without X as a source and basis for X, then X has no meaning and no purpose".
    Also, just for information's sake, I'm not an "atheistic evolutionist". I happen to be a religious jew. But I'm an honest one - which means that I do not play stupid games like Dembski in order to create fake justifications for my religion.

  • Bronze Dog says:

    Note how skye neglects to put any content into that post. Just pseudo-intellectual gymnastics.
    I'm curious how he thinks the lack of definition for "intelligence," a term evolution doesn't really need, affects anything.

  • Anonymous says:

    skye,
    Evolution isn't atheistic any more than remaining science. Science is a tool, and tools are secular - a hammer doesn't care what it hits. (If you are uncertain, the legal world thinks so too. The US constitution separates a secular state and religions to make religions free for everyone - so science couldn't be taught in US schools if it wasn't secular.)
    If you mean that Dembski is trying to justify a belief on the wrong grounds - yes, creationism is bad theology since it tries to use 'facts' to justify a belief, and those 'facts' are necessarily wrong since they are grounded on beliefs. In this case provably so since evolution is a fact.

  • Torbjörn Larsson says:

    For some reason my last comment become anonymous.

  • Roger Rabbitt says:

    I happen to be a religious jew. But I'm an honest one - which means that I do not play stupid games like Dembski in order to create fake justifications for my religion.

    Honest? What about this comment upthread?

    Dembski is under the impression that anything that isn't completely random must be the product of intelligent selection.

    Putting aside the implication that you can read his mind, his arguments are filled with references to lawlike behavior that don't trip the design inference.
    And then we have this comment elsewhere in your blog:

    But what if Demsbki defines specification and complexity as the same thing? Then his definitions are wrong: because he requires them to be distinct concepts, but he defines them as being the same thing.

    I understand that this kind slop appeals to your choir, so feel free to have at it. But it is clearly dishonest and playing stupid games.

  • Roger:
    I seriously challenge you to find anywhere in the history of my blog, here or at blogger, where I've been less than honest. Abrasive, insulting, argumentative, even arrogant and obnixous - those, I wouldn't argue with. But dishonest? Put up or shut up.
    The first comment you quote upthread *isn't me*. Don't play the game of trying to claim that I'm dishonest by dishonestly claiming that I said something that was said by someone else! There are plenty of comments on the blog that I don't agree with - I don't censor comments. People are responsible for their own words. If I said it, I'll take responsibility for it. If I didn't say it, then don't attribute it to me.
    The second line you quote is perfectly accurate. Dembski may not have *intended* it that way; he may not even understand that that's an implication of his own argument. But it is *not* dishonest to point out that he very clearly defines "complexity" in many of his writings as complexity in the information theoretic sense of "high information content"; and then in the paper where he discusses specification, he defines specification as the IT sense of "low information content". You might not like the fact that Dembski screwed up that badly, but it's not dishonest to point out that Dembski's own writings have defined specified complexity in a contradictory way.

  • Roger Rabbitt says:

    The first comment you quote upthread *isn't me*. Don't play the game . . .

    You are correct. I made a mistake. In reading the exchange, I assumed the posting was yours, and didn't check the name at the end. My humble apologies.
    Having said that, I don't shrink from the charge I made. But I'll take up your challenge in the other thread (Dembski's Profound Lack of Comprehension of Information Theory) since that posting will be the focus of the dispute.

  • Kerry Soileau says:

    I have a question about evolution that I have been puzzling about for a while and would like to get feedback about it.
    There is a surgical procedure called a hemispherectomy (http://en.wikipedia.org/wiki/Hemispherectomy), in which half of the brain is removed. This drastic operation is sometimes done to treat severe epilepsy in children. Amazingly, recovery is usually near-complete. This healing capability of the body seems impossible to have been acquired through evolution, since the procedure has been done in only the last tiny fraction of human history, hence a long evolutionary process could not account for it.
    In general, how does one account for the body's ability to heal from surgical "injuries" which humans have experienced only in relatively recent times?

  • Mark C. Chu-Carroll says:

    Re #16:
    What makes a surgical injury any different from any other injury - other than the fact that it's very done very precisely, and in a sterile environment?
    If there's nothing substantially different, then why would a surgical injury require a different healing mechanism than any other injury?

  • Kerry Soileau says:

    @17:
    Because many, if not most injuries resulting from surgery do not occur accidentally and did not occur at all until very recently in human history. So it seems difficult to use evolutionary processes to account for the body's ability to heal from them.
    To put it another way, since humans have accidentally broken bones for millennia, it seems reasonable to assume that the body "learned" to mend bones through evolution. But how could the body know how to reconfigure half a brain to work nearly as well as a whole brain, without many (survivable) brain injuries to "learn" from. I say survivable because dead persons don't pass their genes on to the next generation.

  • Skemono says:

    Because many, if not most injuries resulting from surgery do not occur accidentally

    Utterly irrelevant. Your body can't tell the difference between being punctured accidentally and being punctured with intent. It's the same phenomenon, and the body has the same response to it.

    But how could the body know how to reconfigure half a brain to work nearly as well as a whole brain, without many (survivable) brain injuries to "learn" from.

    Ugh. Your misconceptions are staggering, and I don't think I could really address them all. You'd probably be better served asking this question of a biologist or neurosurgeon than a computer scientist. Steven Novella of NeuroLogica Blog addressed this phenomenon in a recent post.

  • Mark C. Chu-Carroll says:

    Re #18:
    How does your body know the difference between an "accidental" damage and deliberate surgical damage?
    People have been damaging their brains forever. Serious falls, fights, animal attacks, etc., all have the potential to do brain damage. Hell, I've got a little patch of scar tissue in my brain from oxygen deprivation when I was being born. It's incredibly common.
    The only real difference between having part of your brain damaged by getting hit by a rock, or getting it cut out, is that the surgical one is more precise and sterile.
    The surgical one is easier to recover from - precisely because of those two differences. The "damage" from surgery isn't just random. It's not some random region of brain tissue that was damaged. It's deliberate - done to remove/alter a specific piece of tissue for a specific region. And healing from a clean surgical wound that was kept sterile is a lot easier that healing from a ragged injury.

  • Kerry Soileau says:

    @18: Ugh. Your utter inability to understand my question is staggering. Maybe remedial reading will help. Good luck.
    @20 Until modern times, NO ONE recovered from an accident that resulted in half of their brain being removed from their cranium. So natural selection never had an opportunity to develop the observed ability of the brain to recover from such an event. Hence evolution could not have been the cause of the body's observed capability to rewire half a brain to take over the functions of a removed other half.

  • Mark C. Chu-Carroll says:

    Re #21:
    Until modern times, no one recovered from an accident that *specifically* resulted in half of their brain being removed. But the way that our brains work, they're very good at adapting to compensate for all sorts of damage. The brain doesn't have a specific set of "If this specific injury happens, this is how to work around it". Instead, it's a network which is self-adaptive, and works around damage - faced with any kind of damage, it will *attempt* to adapt to work around the damage.
    You're just creating a strawman - demanding that the brain must have a *specific* response to this *specific* injury. It doesn't.
    What the brain has is a *general* response to damage. That response is sufficiently powerful to allow it to adapt to all sorts of damage - even very serious, profound damage.
    On the other hand - the surgery you're talking about isn't nearly as perfect as you make it out to be. The people who've been through it have had *profound* disabilities all of their lives due to epilepsy.
    According to the wikipedia entry *you* cited, pretty much everyone who gets that surgery winds up with some amount of paralysis, and many also wind up with vision problems. They also frequently have severe learning difficulties. And it only really works in young children, whose brains are still very in a state of development plasticity.
    In other words, your argument is completely bogus. You can't completely recover from that. You can recover amazingly well if its done when your brain isn't fully developed - in which case the recovery follows *exactly* the typical neurological healing response to *any* brain injury. There's nothing special about it.

  • Skemono says:

    So it looks like you didn't bother following the link I gave you, huh? The one that explains how brains actually work and how one that's still forming could recover from being harmed?
    No, of course not. Why bother educating yourself rather than repeating nonsensical questions rooted in a dismal misunderstanding of how evolution and biology actually work?

  • Kerry Soileau says:

    @22:
    "In other words, your argument is completely bogus."
    LOL Typical. I ask a perfectly reasonable question. You don't know how to answer it. So you relabel it an "argument", and call it bogus.
    And to think I thought Google hired only intelligent people.
    Enjoy your ignorance. If I find an actual answer to my question, from someone who knows what they're talking about, I might post it here.
    Or not.

  • Mark C. Chu-Carroll says:

    Re #22:
    (A) Whether your question was "perfectly reasonable" is actually arguable. If you were posting in, say, a neurophysiology forum, it would definitely be absolutely reasonable. But you posted a question about neurophysiological healing on a math blog, in a post critiquing William Dembski's "No Free Lunch" theorems. In other words, you posted an off-topic question in a forum that where you had no reason to expect anyone to have the background to answer it. Is it perfectly reasonable to ask an off-topic question in an inappropriate forum?
    (B) Your question was answered, multiple times. The fact that you don't like the answer doesn't change the validity of the answer. You wanted to know how evolution can explain why people who get hemispherectomies can recover completely. The answer to that is that (A) people don't completely recover; and (B) we didn't evolve a *specific* healing response to a specific kind of neurological surgery; our brains have a *general* adaptive response to damage which is particularly effective during early development. The surgery you asked about is just a particularly extreme form of damage - but our bodies respond to it like they would to any other damage.
    (C) A question becomes an argument when the question is answered, and you start arguing with the responses. You *are* arguing that surgical alterations to the brain are fundamentally different in kind from any other kind of damage to the brain, and that healing/adaptation responses to any other kind of damage cannot be applied. If you can't make that argument, then your "question" has been answered.
    But instead of actually listening to the answers that multiple people have posted, reading the sources that have been cited, you're just doing the rhetorical equivalent of putting your fingers in your ear and shouting "la la la I can't hear you".

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