I've gotten my hands on a review copy of Michael Behe's new book, "The Edge of Evolution". The shortest version of a review is: Bad science, bad math, and bad theology, all wrapped up in a pretty little package.
As people who've followed his writings, lectures, and court appearances know, Behe is pretty much a perfect example of the ignoramus who makes a bad argument, and then puts his fingers in his ears and shouts "La la la, I can't hear you" whenever anyone refutes it. He still harps on his "irreducible complexity" nonsense, despite the fact that pretty much every aspect of it has been thoroughly refuted. (The entire concept of IC is a pile of rubbish; the entire argument about IC is based on the idea that evolution is a strictly additive process, which is not true; there are numerous examples of observed evolution of IC systems, both in biology and in evolutionary algorithms. But none of these facts makes a bit of difference: like the energizer bunny of ignorance, he just keeps going, and going...)
Anyway, the new book is based on what comes down to a mathematical argument - a mathematical argument that I've specifically refuted on this blog numerous times. I'm not mentioning that because I expect Behe to read GM/BM and consider it as a serious source for his research; even if I were an expert in the subject (which I'm not), a blog is not a citable source for real research. But I mention it because the error is so simple, so fundamental, and so bleeding obvious that even a non-expert can explain what's wrong with it in a spare five minutes - but Behe, who apparently spent several years writing this book still can't see the problem. (In fact, one of the papers that he cites as support for this ridiculous theory contains the refutation!)
Behe's argument is that what's commonly referred to as the theory of evolution is actually made up of three parts:
- Common Descent: all living creatures are derived from common ancestors by modification. I'm not quoting Behe's explanation of this here, because it's astonishingly muddled for such a simple idea: he's so eager to start throwing in his digs at the idea of evolution that he muddles the explanation of common descent with irrelevant gibberish. In fact, his explanation of this reads almost like an endorsement of John Davidson's "prescribed evolution".
- Natural Selection: Michael Egnor's favorite. As Behe states it (on page 2 of TEoE), "the idea of natural selection says just that the more fit organisms of a species will replace the progeny of the less fit".
- Random Mutation: again, quoting Behe: "the only way a plant or animal becomes fitter than its relatives is by sustaining a serendipitous mutation." In the expansion of this, he handwaves his way around, basically asserting not just that mutation is random, but that the only kinds of mutation are single-point changes: no duplication, no frameshifting, etc.
This is already poor stuff - the muddled version of his explanation of common descent; his presentation of a shallow tautological form of natural selection; and his ignorance of any source of genetic diversity other that mutation.
As soon as he gets through that muddled explanation, he starts to launch his attack in earnest. And it's a sad attempt:
In the past hundred years science has advanced enormously; what do the results of modern science show? In brief, the evidence for common descent seems compelling. The results of modern DNA sequencing experiments, undreamed of by nineteenth-century scientists like Charles Darwin, show that some distantly related organisms share apparently arbitrary features of their genes that seem to have no explanation other than that they were inherited from a distant common ancestor. Second, that random mutation paired with natural selection can modify life in important ways. Third, however, there is strong evidence that random mutation is extremely limited. Now that we know the sequences of many genomes, now that we know how mutations occur, and how often, we can explore the possibilities and limits of random mutation with some degree of precision--for the first time since Darwin proposed his theory.
This is a careful verbatim quote from his book. What I found astonishing here is that he asserts his conclusions in this paragraph as settled fact, without even attempting to cite any evidence. It's typical, but pathetic. It's not like he doesn't use citations and footnotes through the book - he sometimes insert supportive citations of completely trivial things. But this incredible statement: that "there is strong evidence that random mutation is extremely limited", he doesn't even attempt to support.
The rest of the book focuses an this alleged problem: that random mutation is somehow constrained, and can't produce the necessary changes to explain the diversity of life.
The part of the book that is most annoying to me, and thus the part that I'll focus the rest of this review on, is chapter three, "The Mathematical Limits of Darwinism". This is, basically, the real heart of the book, and for obvious reasons, it seriously ticks me off. Behe's math is atrociously bad, pig-ignorant garbage - but he presents it seriously, as if it's a real argument, and as if he has the slightest clue what he's talking about.
The basic argument in this chapter is the good old "fitness landscape" argument. And Behe makes the classic mistakes. His entire argument really comes down to the following points:
- Evolution can be modeled in terms of a static, unchanging fitness landscape.
- The fitness landscape is a smooth, surface made up of hills and valleys, where a local minimum or maximum in any dimension is a local minimum or maximum in all dimensions.
- The fitness function mapping from a genome to a point of the fitness landscape is monotonically increasing.
- The fitness function is smoothly continuous, with infinitessimally small changes (single-point base chanages) mapping to infinitessimally small changes in position on the fitness landscape.
Of course, Behe doesn't phrase it like that; in fact, I doubt that he even understands that he's making those assumptions: His grasp of math is extremely shallow, and his mathematical reasoning is glib at best.
First, I'll repeat what I've said in the past about what's wrong with each of these assumptions. Then I'll put out a couple of examples in the text of how Behe attemps to refute these criticisms, and show what's wrong with them.
Behe uses these assumptions about the fitness landscape, and the search process which is his model of evolution, to build his argument. He frequently talks about how things can get trapped at a local maximum. By Behe's reasoning, once a species reaches a local maximum of a fitness landscape, that's the end of any process of change in that species. When he talks about a limit of what can be done by mutation+selection, that's what he's talking about: the idea that local maxima are traps.
This is one of the oldest canards of the IDists: the mis-modeling of evolution as a search process over a static landscape. The problems with this are quite simple:
First, It assumes that the fitness landscape is fundamentally low-dimensional. If the fitness landscape truly has many independent dimensions, then there are very few (if any) true local maxima. To assume that local maxima are common requires assuming that when moving through one dimension brings you to a local maximum, moving through any other dimension will also bring you to a local maximum at the same point - which is really another way of saying that the dimensions are not independent - they all reach maxima and minima at the same places.
The idea of local maxima and minima being common comes from thinking of things in terms of low-dimensional surfaces. A fitness landscape with two variables forms a three dimensional graph - and in three dimensions, we do frequently see things like hills and valleys. But that's because a local minima is the result of an interaction between only two variables. In a landscape with 100 dimensions, you don't expect to see such uniformity. You may reach a local maxima in one dimension - but by switching direction, you can find another uphill slope to climb; and when that reaches a maximum, you can find an uphill slope in some other direction. High dimensionality means that there are numerous directions that you can move within the landscape; and a maximum means that there's no level or uphill slope in any direction.
(As an interesting aside, IDists, when they're quoting Dembski, like to talk about the No Free Lunch theorems. The NFL theorems are based on the idea that landscapes really aren't smooth - that they don't have uniform properties that permit a search strategy to work. Behe's argument totally contradicts that - the kinds of landscapes that must be considered to make NFL work totally devastate Behe's idea. )
Second, Behe assumes that the landscape can't change. If it's a local maximum today, it's a local maximum tomorrow. The reason that he needs this is obvious: if todays local maximum can stop being a maximum, then it's not any kind of a barrier. The argument requires that the landscape never change.
This is the biggest problem with the whole idea of modeling evolution as search over a fitness landscape: landscape search generally assumes a static landscape. But this doesn't match reality at all. Just consider a simple example. Suppose you've got a local maximum in the landscape, and that that maximum represents a fitness point for a plant-eater: that point represents an adaptation to a diet that's based on some kind of vegetation, and a behavior that protects it from predation. Because it's a maximum, things that get anywhere near it end up climbing the slope to that maximum. The local maximum becomes a clustering point for plant-eating species. The fact of that clustering means that the population at that point is going to grow.
The growing population means that you'll be creating another fitness point on the landscape: a point for a predator. That point didn't exist before: when there wasn't a population of plant-eaters for a predator to consume, there would be no advantage to evolving to fit the niche of eating the creatures that eat the vegetation; once there is a population of plant-eaters there, then you've got a new fitness point.
The growing population also means that the fitness of that point may start to decline: too much competition for the resources. Too many creatures trying to eat the same limited food source.
This is the reality of the "fitness landscape": the landscape is shaped from the species that inhabit it; as the species change, the landscape changes. Those traps that Behe keeps talking about only exist if the landscape doesn't change. But the only way that the landscape doesn't change is if the species in it don't change. The moment any species starts climbing a hill in the fitness landscape, the landscape must change to describe the new circumstances.
Third, Behe, as in his IC gibberish, insists on a monotonically increasing fitness function, and he insists on mutation behaving as a continuous function. According to Behe, the only changes are changes that produce an immediate increase in fitness. So if you're at a local maximum, there's no way to escape it, because you can't go downhill. There are two problems here: one is that it's possible for a species to become less fit; the other is the continuity assumption.
With respect to that first issue, it's possible in many circumstances, for a population to become less fit. When a species is not under strong selective pressure, it's possible for numerous neutral or even slightly negative mutations to accumulate in the population. There's nothing in reality preventing that: mildly negative mutations do occur in reality. In Behe's model, that means that in reality, evolution isn't a strict hill-climber; crossing a valley to get to a higher fitness summit is not impossible.
The second part if this is a huge problem for Behe's argument. Behe wants to be able to argue that local maxima are traps. A local maxima is only a trap for a search process if the search has certain strict limitations: the search needs to behave as an almost continuous function. This is a bit messy, because we're straddling the line between continuous math and discrete math here. But the idea is that Behe's model is that there's a function from a species genome to a point in the fitness landscape; and that mutation makes an small change to the genome, and that that small change to the genome must correspond to a proportionately small change in the mapped location on the landscape. So mutations can only produce small changes; and small changes can only result in small motions on the landscape. That means that the evolutionary search process can't jump valleys in the landscape.
The problem is, that doesn't correspond to reality. There are times when a small change can have a huge impact. The classic textbook example of this is the Panda's thumb: a very small genetic change caused a change in the developmental process in the wrist of the panda, which produced what is effectively an extra thumb. The genetic change that produced this is tiny; the effect is huge. This is not an unusual thing: small changes can have huge effects. But small changes with large impacts totally blow Behe's argument out of the water: they mean that Behe's barriers aren't barriers at all.
So Behe's argument fails miserably, because it's built on a pile of obviously invalid, long-discredited assumptions. And yet he builds his entire book around them - and just acts as if the assumptions were obviously correct, and no one has ever refuted them. Even when the sources that he cites contradict him, he acts as if there's nothing wrong: he cites several papers about modeling evolution with a fitness landscape that specifically discuss the dimensionality issues, and then in the same paragraph as the citation, talks about the fitness landscape as a surface in three dimensions. The only explanation I can find for his is that he really doesn't understand most of the math that he's talking about. (I don't think that Behe is above deliberately lying; but I think he's smart enough that he wouldn't cite things that contradict him so blatantly if he understood what they really said.)
Behe isn't entirely ignorant of the criticisms of the landscape arguments - he does devote some space to arguing around them. Anyone care to guess what kind of argument he uses? Anyone?
What's the favorite bullshit mathematical argument of creationist assholes worldwide? Why big numbers, of course! He starts to slap together some sloppy probabilities to argue how unlikely it is for a mutation to jump valleys in a fitness landscape. He goes through a really sloppy argument about how unlikely it is for malaria to evolve chloroquine resistance, arguing that the odds of evolved resistance are one it 1020. Now, when you realize that each person infected with Malaria has billions of malaria cells in their bodies, and that number starts to not look so scary anymore: billions of cells reproducing daily in millions of individuals, which has been going on for decades of chloroquine use, and you start to realize that that's not such a big number after all. But even so - it's a deliberately inflated number, relying on things like the monotonicity assumption, and the assumption that resistance is all-or-nothing. But even with those sleazy assumptions, that number just isn't compelling when it comes to malaria. So, he tries to take the inflated malaria number, and wave his hands around by applying it to human beings, because we reproduce so slowly compared to malaria:
If all of these huge numbers make your head spin, think of it this
way. The likelihood that Homo sapiens achieved any single mutation
of the kind required for malaria to become resistant to chloro-
quine--not the easiest mutation, to be sure, but still only a shift of two amino acids--the likelihood that such a mutation could arise just
once in the entire course of the human lineage in the past ten million
years, is minuscule--of the same order as, say, the likelihood of
you personally winning the Powerball lottery by buying a single ticket.
What's particularly astonishing about this is that even this rotten argument - taking an artifically inflated probability number based on the peculiarities of the biochemistry of one specific organism, and applying it to a completely different organism (waving hands furiously to try to distract from the fact that it's just nonsensical to cross that way), contains its own refutation. Yes, perhaps the odds of this happening are similar to the odds of winning at powerball. But the fact is someone wins the powerball lottery. He wants to pretend that it's unlikely by pointing at you specifically, and saying that it's like you winning the lottery. But in fact, the power of evolution is that it doesn't just try one thing. It's not a process of one mutation, wait and see if it works out and fixes in the population; it's not a process with a predetermined destination. It's a process of countless mutations happening at the some time - some propagate, some don't - and if any of them work, then they take over. The real chance of evolution producing something are like the chances of someone winning the lottery. The chances of them producing humanity taken a priori are like the chances of you winning the lottery; but since humanity was not a predestined result, the chances of the evolutionary sweepstakes producing something is like the chances of someone winning the lottery - i.e., virtually inevitable.
Finally, I said that not just is Behe's book bad science and bad math, but it's bad theology. Behe claims to believe in an all-knowing, all-powerful God. But at the same time, his entire book is based on the argument that God created life on earth, and got it all going using an evolutionary process. But then, according to Behe, over and over again, his creation was woefully inadequate of facing the actual challenges that it would face, and so his all-powerful creator needs to constantly intervene, and tweak things in order to make them work. His God is a buffoon - a bumbling fool who isn't capable of creating worlds in a way that works. Reading his book, I'm actually shocked that he's a religious person: he's clearly never bothered to think through his beliefs, and what his theories say about them. Again and again, reading the book, I kept finding myself saying two things: "How can this guy call himself a scientist, when he argues so sloppily?", and "How can this guy be religious when he apparently believes that his creator isn't capable of getting anything right?" Following Behe's argument, it seems like it should be impossible for Behe's god to have done the things Behe claims that he did, because they're too hard for such a bumbler.
I'm sure that that aspect of Behe's book isn't deliberate. But it's typical: he seems to be incapable of actually really thinking about an argument in any way deeper than asking "Does this agree with my conclusion?"; and even then, he doesn't seem capable of recognizing when an argument doesn't support his conclusion. It's really appalling. Frankly, I'm really shocked that this guy ever managed to get tenure anywhere - judging by his writing, he's not particularly bright; he's a remarkably disorganized and muddled thinker; and he's incapable of comprehending or responding to arguments made by other researchers.
(Note: several typos: a missing "not", a missing "resistance", and "got" for "god", "lest" for "less" were corrected in the above. That's what I get for trying to write in short bursts while waiting for builds.)
Comments
Edit:
The word "resistance" should follow chloroquine.
Imputing teleology to evolution?
Posted by: Blake Stacey | May 31, 2007 12:42 PM
Thanks for taking the time to do the review - I hope you were in proper anti-odor gear when reading his "book". It seems to me that Behe is clearly saying "I am in it for the money" and his creo / DI overlords are willing to give it to him to shore up their diminishing post-Dover world.
Posted by: J-Dog | May 31, 2007 12:51 PM
Do you really intend the word "predestined" here? I think that you are saying something other than what it sounds like--I think you are saying that it may well be that the chance of evolution producing something like humanity are small a priori (which may or may not be true), but we can't apply that in reverse to argue that the existence of humanity is inconsistent with evolution, in the same sense that the probability of any particular individual winning the lottery is very small, but we cannot argue from the fact that a particular individual did win the lottery that the drawing was rigged. But I still wouldn't say that that individual was "predestined" to win.
Posted by: trrll | May 31, 2007 12:55 PM
Typo:
Posted by: Blake Stacey | May 31, 2007 12:56 PM
trrll:
Stupid typo - left out a "not"!
Posted by: Mark C. Chu-Carroll | May 31, 2007 1:09 PM
Posted by: IanR | May 31, 2007 1:23 PM
I live within the Christian community, and I can assure you that the content of this book is completely irrelevant--all that matters is the book's existence. Christians will thumb through the book and see big words and diagrams, and they will imagine all those wicked evolutionists shaking there fists and yelling "That Behe is ruining everything!" Students at Christian schools will quote this book--without understanding it--in their assignments, trusting that, whatever it says, it somehow refutes evolution. At no point will the "science" be examined.
I know this because I was once one of those students.
Posted by: RoaldFalcon | May 31, 2007 2:04 PM
Great review! (and another typo: lest fit?)
Posted by: pough | May 31, 2007 2:19 PM
"He goes through a really sloppy argument about how unlikely it is for malaria to evolve chloroquine resistance, arguing that the odds of evolved resistance are one it 10^20."
This is weird. How did it evolve? Has God intervened in the last few decades? Is he basically moving on to reject even microevolution?
Posted by: SteveF | May 31, 2007 2:53 PM
SteveF:
I'm really not sure.. He's amazingly cagey about things. For example, the way that he defines common descent isn't what most people would mean by common descent - he really ultimately defines it as the fact that there's a nested hierarchy of common features, *not* that things are descended from a common ancestor.
But WRT the chloroquine resistance, it seems like his argument isn't against microevolution. It's that even a small change like that requires a huge number of generations to make it possible, and that while that's possible for something with quadrillions of individuals reproducing every day, if you try to apply the same probabilities to primates, which have 6 or 7 orders of magnitude fewer individuals, and whose generations are decades not hours/days, that even small changes become too improbable to consider. So he's pretty much arguing a classic christion position, that while something like evolution might work for those lowly animals, we humans are *special*, and what works to explain variations in animals can't work to explain us.
In other words, it's a shabby "gosh aren't we humans amazing, God must have made us" argument from incredulity. So when his argument about reproductive barriers gets knocked to pieces, he basically tries to duct tape them back together with big numbers and human chauvinism.
Posted by: Mark C. Chu-Carroll | May 31, 2007 3:03 PM
Sounds like he read my HOWTO.
Posted by: MarkH | May 31, 2007 3:19 PM
I have a feeling Behe isn't being fully honest. His god makes even less sense than the god of the fundamentalists. His is not a particularly intelligent designer, but rather an inept tinkerer. He created life through an evolutionary process, but the process doesn't work to do anything much, so he ended up having to do most of it manually anyway. While that may not be logically inconsistent, it surely doesn't sound particularly compelling.
Occam's razor would lead me to speculate that it's much more likely that he doesn't believe in a god like that at all. Rather, that is the only god he can, with much handwaving and willful ignorance, conjure to fit the data. It seems probable that Behe doesn't believe his own bullshit, and that he's nothing more or less than another in a long line of pious liars.
Posted by: Rev.Enki | May 31, 2007 3:46 PM
Brilliant review. Keep it up.
Posted by: Donald | May 31, 2007 3:56 PM
You missed an important criticism of his landscape argument.
Individuals are the main level of selection, not populations. So instead of mapping a population genome to a point on the landscape, you map each individual's genome to a point. Populations at local maxima are not a point at the maxima, but a cloud "centered" on it. As Wright pointed out when he developed the landscape analogy in the 1930's, even on static landscapes, it is possible for outliers of a population at a local maxima to find another peak and their descendants can climb up it.
Posted by: Reed A. Cartwright | May 31, 2007 3:57 PM
Hmm, I hope for your blood pressure you didn't have too many bugs.
One question -
Monotonically increasing in what? This seems to contradict point 2 (that there are local maxima). Do you mean that the mean fitness of the population is monotonically increasing in time (i.e. from Fisher's Fundamental Theorem)?
Oh, and just because I'm a pedant - a few maxima should be singular maximum(s).
Other than that, it was a fun read: I guess I won't have to read the original, then.
Bob
Posted by: Bob O'H | May 31, 2007 4:04 PM
The part of the book that is most annoying to me, and thus the part that I'll focus the rest of this review on, is chapter three, "The Mathematical Limits of Darwinism". This is, basically, the real heart of the book, and for obvious reasons, it seriously ticks me off. Behe's math is atrociously bad, pig-ignorant garbage - but he presents it seriously, as if it's a real argument, and as if he has the slightest clue what he's talking about.
In that respect Behe is following the footsteps of his "favorite mathematician" and friend William Dumbski. Put some numbers and equations together, make it look "sciency" and the gullible will bite it. Pathetic.
Posted by: Tyrannosaurus | May 31, 2007 4:08 PM
It strikes me as a strange argument; if he is arguing that the evolution of malarial resistance is extremely unlikely given the probabilities supposedly involved, yet it happened anyway, what the hell is the point in talking about probabilities in the first place.
The odds of me being born are pretty small, but I'm sitting here right now.
Posted by: SteveF | May 31, 2007 4:09 PM
SteveF: well, he's saying the probability of malarial resistance evolving without god's help are tiny. So the 'it happened anyway' doesn't apply because, in his mind, god did interfere.
Posted by: Olaf | May 31, 2007 4:41 PM
Reed is pointing in the right direction (it send me back to undergrad times). The maxima could be compared to an "average-of-some-sort" (but not exactly) centered in the values exhibited by the individuals in the population. So you can have "outliers" reaching towards other peaks.
Posted by: Tyrannosaurus | May 31, 2007 4:41 PM
[Off topic]
"while waiting for builds."
What? You mean Google doesn't have some kind of distributed build system in place?
Posted by: Gerald Squelart | May 31, 2007 6:07 PM
I suspect Behe's not as dumb as his arguments would lead one to believe. The point is to give the ignorant/gullible something that sounds smart to lend credibility to the argument. For his audience, making any argument is as good as making a solid argument. I'm sure he really believes in creationism, but he might very well know his arguments are BS. He's not out to convince smart people, just a slight majority of all people. I also suspect he feels his goals are noble, so the means are justified. Plus, he makes some money along the way.
Posted by: Bill | May 31, 2007 6:30 PM
A good read whether it captures mere parts of Behe's book or not.
Part of the reason creationists like Behe get stuck on a constant fitness landscape ;-) is that they can't envision or acknowledge other species evolving. I doubt Behe has internalized what his earlier admission of microevolution means in these terms, much less his prophetized 'goddidits' of new species.
More of the same thing. The basic observation of nested hierarchies of features (in characteristics of fossils or sequencing of genomes) is the fact that he must admit, while the consequent universal mechanism of descent by inheritance is what he can't affirm.
Behe is a splendid case of denialism, making his lone balance act on the edge of evolution.
Posted by: Torbjörn Larsson | May 31, 2007 7:38 PM
The average human carries a mix of "good" genes, and a goodly number of so-so ones.
Hopefully, most of our weak genes will be recessive, so not much of an hindrance.
Alao there is vast redundancy in our whole organism, many people manage to live a normal live even missing important proteins, on a back-up system, or the back-up of the back-up.
And, thru the mutation lottery, any of our weak genes can be promoted to a superior gene (in our offspring). Or even, assume a totally new functionality.
Posted by: _Arthur | May 31, 2007 8:02 PM
Posted by: Token | May 31, 2007 8:09 PM
Token:
Yes, I did mean infinitessimally. From his discription, Behe's landscapes are low-dimensional continous integratable curves, and his notion of motion across them is of essential continous smooth motion: each step is nearly infinitely small - in fact, he's quite explicit that his notion of mutation (the cause of motion in the landscape) does not permit anything but the smallest possible changes. So my image of it is very calculus-like: a continuous, differentiable curve, with motion over the curve described in terms of infinitessimals.
Posted by: Mark C. Chu-Carroll | May 31, 2007 8:18 PM
You're right about various things, like the fact that the fitness landscape is far from static. However, your argument about local maxima being rare in high dimensions is incorrect. Generic high-dimensional functions do indeed have vast numbers of local optima, and I don't see any conceptual reason why fitness landscapes shouldn't. (For example, convexity could be a good reason, but that's not true.) Is there something I'm missing?
Your argument seems to me to work just as well in two dimensions as in 100. If you pick a one-dimensional slice and look for a critical point along that slice, then there's no reason why it should be critical in the perpendicular direction. (This is the core of your argument about reaching a local maximum in one direction but then getting to switch direction.) However, that doesn't mean there aren't lots of critical points for the unrestricted function. If f is the objective function, then the points where df/dx vanishes generically form curves, as do those where df/dy vanishes. If the function is complicated enough, then these curves will wiggle around a lot and one expects them to cross in many locations. At these crossing points, df/dx=df/dy=0 so these are critical points. (I'll address whether they are maxima in a moment.)
The same thing happens in high dimensions. The sets on which each of df/dx_1,...,df/dx_n vanish are hypersurfaces, and one expects these hypersurfaces to intersect in a large set of points. In very loose terms, if each hypersurface wiggles back and forth k times across the fitness landscape, then one expects about k^n intersections. Aside from polynomials I don't know how to make this rigorous, but the intuition is good. Of course we wouldn't expect these critical points all to be local maxima: if we assume the eigenvalues of the Hessian are independent and each 50% likely to be positive (a bogus assumption but a decent first guess), then we expect about a 1/2^n fraction of the critical points to be local maxima. If we have k^n critical points with k>2, as we would expect for sufficiently complicated functions, then we expect an exponential number of local maxima.
In practice, most continuous optimization problems in high dimensions do have vast numbers of local optima, unless some phenomenon like convexity intervenes. (Note that the heuristics above break down for convex functions: k=1, so we expect only one critical point, and the eigenvalues of the Hessian are far from independent.)
This profusion of local maxima doesn't matter: we know from physics that nature is just as happy to sit in a local optima as in the global optima. And of course you're right that there are much deeper problems with Behe's arguments (such as assuming a static fitness landscape, which is ridiculous).
Posted by: Anonymous | May 31, 2007 9:10 PM
I wish behe and dembski would just make the one authoratative book so ID wasn't impossible to criticize just because it's a moving target ... oh ... wait ...
(and "a local minima" should read "... minimum"
Posted by: snaxalotl | May 31, 2007 10:06 PM
My experience with multi-dimensional solution spaces from the field of evolutionary computation suggests that local maxima are ubiquitous, and are a great problem in the real fields of "intelligent design": electrical, aerospace, chemical and all the other forms of engineering. The idea of a constant fitness landscape is of course laughable, but instead of claiming that "it's possible in many circumstances, for a population to become less fit," wouldn't it be better to point out that any given gene pool is chock full of less-than-optimal alleles?
We can offer many examples of local maxima: the poor configuration of our own bodies is one, but it doesn't mean that Behe can extrapolate this idea to stupidity.
Posted by: John Vreeland | May 31, 2007 10:33 PM
Technorati hasnt picked up on it yet-- but I drew some beautiful diagrams for the fitness landscape of HIV :) If Ive misspoken on fitness landscapes, I would greatly appreciate the criticism!
Posted by: ERV | May 31, 2007 10:40 PM
I would like to support anonymous and John Vreeland. Local optima in higher dimensional space do occure frequently, and search algorithms will not use the "search one dimension, then the next" approach, they would more likely use the set of partial derivatives at a point to derive a vector direction for maximum increase (or decrease for minima) and base a search algorithm on that.
I have a larger issue both with Behe and yourself in that both of you seem to regard the "fitness landscape" as a real (as in actual) function. As I understand it, the concept was only ever intended as an illustration to help in the understanding of evolution. We know few of the actual function's properties. It's far from obvious that knowing them would provide anything of much predictive power, since for large bodied organisms at least we're talking immense periods of time simply to validate them. It's possible that investigating the function's properties locally for single celled organisms might turn up something useful, but somehow I doubt that it would be more than is already being done in biology and medical research facilities already.
In short, both Behe and yourself are arguing about a chimera, which to me is somewhat silly.
Posted by: DavidSR | May 31, 2007 11:42 PM
So is Behe actually arguing that the Generator Of Design intervened personally to miraculously confer chloroquine resistance on the malaria parasite? Hardly seems benevolent. Isn't that taking the "not a sparrow falls" business a bit to an extreme?
Posted by: trrll | May 31, 2007 11:48 PM
Stuart Kaufman has done some very interesting simulations of theoretical fitness functions. Some of his results suggest that there are limits to the complexity of organisms (technically the number of interactions between different genes) that are capable of evolving, above which the fitness function becomes too uncorrelated for heuristic searches like natural selection to be efficient. This brings up an additional point--there is selection for evolvability. Organisms that are incapable of evolving efficiently by natural selection will be unable to track their fitness optimum when the landscape shifts (e.g. a new disease or predator emerges) and are at increased risk of extinction.
One thing mutation studies have demonstrated is just how robust organisms are to mutation. Very often, biologists knock out a gene that is believed to have a crucial function and the organism turns out to be virtually normal due to compensation occurring in development. And in a recent study, the brains of transgenic mice engineered to express an additional photopigment in the eye exhibited improved color vision, demonstrating that the developing mouse brain was able to adapt to take advantage of the "mutation." This is just the sort of thing that is expected if there is selection at the species level for 'evolvability.'
Posted by: trrll | June 1, 2007 12:27 AM
Well Hell, Mark, you wrote (a good part of) the review I was making notes for. So I guess I'll have to salvage the parts you didn't cover -- Behe's dismissal of computer simulations of evolutionary processes -- and make do with that. :)
With respect to the discussion of the prevalence of local maxima in high-dimensioned spaces, I found it interesting that Behe used a figure from Gavrilets' book, but apparently didn't actually read the book, since Gavrilets argues (contra one or two people above) that higher dimensioned fitness landscapes are rich with neutral ridges connecting most parts of the landscape to most other parts (apologies for the reification).
Posted by: RBH | June 1, 2007 12:44 AM
I have to say that I too believe that in general higher degree functions will have very few extrema... While each partial derivative does define a hypersurface, we will look for places for ALL the hypersurfaces to equal zero, simultaneously. Each partial derivative is its own hypersurface and we must add one more equation that they all have value zero. This is an over-defined system, one where the number of equations to satisfy is greater than the degrees of freedom of the inputs. This means that there will in general be very few solutions, and after that we must take 1/2^(dimension of inputs), for consideration of convexity. Seems small to me.
Posted by: Matthew Bardoe | June 1, 2007 1:17 AM
Excellent review, thanks for writing it. It certainly seems as if Behe hasn't learned a thing from all the fallacies and sloppy mistakes he made in his first book.
Or maybe he *has* learned something -- he has learned that an anti-evolution book doesn't have to make sense or hold up to the slightest scrutiny in order to sell like hotcakes, make a lot of money, and get the author fat lecture fees in front of gullible audiences who will pay to be told what they want to hear.
One minor nitpick about your review -- in the passage "focuses an this alleged", the "an" should obviously be "on".
Posted by: Ichnemon | June 1, 2007 2:27 AM
Regarding Bardoe's comment from 1:17am, the system isn't over-determined: there is one constraint (saying that a partial derivative must vanish) for each variable, so there are exactly the same number of equations as variables. The mistake in the comment is "and we must add one more equation..." (each hypersurface already corresponds to where a partial derivative vanishes, so we don't need any additional constraint to force the value to be zero).
Posted by: Anonymous | June 1, 2007 2:39 AM
Yeah, Behe has somehow managed to be more wrong than Dembski. We should give him some kind of an award for that. If that kind of wrong was in World of Warcraft, its name would be purple.
Posted by: Dustin | June 1, 2007 3:04 AM
The fitness landscape concept is (or was about 10 years ago when I was completing a PhD in behavioural ecology, a field I have since left) certainly used to model evolution of particular characteristics. But usually we'd just be looking at two or at most three dimensions, and one very specific behaviour. So the dimensions in, for example, studying rejection of possible brood parasites might be the probability of another bird laying its egg in your nest versus your own ability to distinguish your chicks from alien chicks and perhaps the cost to you of rearing an alien chick (ie huge if it's a cuckoo, lower if it's a cowbird). It's actually quite a useful way of formalising and quantifying what behaviour you expect under different conditions, leading to testable predictions about what different species should do, instead of just waving your hands and saying behaviour a looks better than behaviour b.
I think part of the problem that Behe is having is that he imagines that for a single organism there is a single maximum, whereas you have to think about all the different charactistics and behaviours that are in some senses being independently acted upon by natural selection. It's not the individual that's sitting on top of a local maximum, it's the sum of each of its characteristics and behaviours, sitting on top of their separate ones.
Even with just that very simple, single behaviour (reject a suspect chick or not), you can get quite complicated functions. But of course each individual has a huge repertoire of behaviour on which natural selection might act, not to mention physical characteristics. And all of them interact with each other. I don't have the mathmatical expertise of the other commenters on this site, but it seems intuitively clear to me that optimising for one single physical characteristic or behaviour on a local maximum definitely doesn't prevent change in another characteristic or behaviour, which could lead to the maximum for the original behaviours being different.
Thinking about it, probably this is just a different way of saying what lots of you have already said about being able to move between maxima in various different ways, but from a non-mathematical biologist's perspective.
Mel
Posted by: Mel | June 1, 2007 6:50 AM
I should have said in my comment above that obviously using the limited dimension landscape is an incredibly simplified way of representing the selection pressure on even just one behaviour, and that assessing even those simple sounding variables is very difficult. I just used it as a tool to help me think clearly about the question I was asking and make some predictions that were more than assertions about one thing being better than another.
Posted by: mel | June 1, 2007 7:01 AM
Reed,
Your point about population maxima, rather than individual maxima is just another way of stating Mark's point about minor non-beneficial mutations (or non-beneficial recombinations of genes from any mechanism for that matter!).
Actually, there's a paper floating around that descibes how sexual reproduction increases the surface of the fitness landscape covered by a population, helping populations escape local maxima. This gives an obvious adaptability advantage to the species involved, hence the preference for sexual reproduction amongst complex species with low reproduction rates...
Posted by: demallien | June 1, 2007 8:14 AM
This is funny...
People who have not ever seen Behe's new book are saying like "Great review!". I can not know, how many strawmen arguments Mark Chu-Carroll have made in his review. But one of his "arguments" was silliest I have heard today. He wrote:
"Behe claims to believe in an all-knowing, all-powerful God. But at the same time, his entire book is based on the argument that God created life on earth, and got it all going using an evolutionary process. But then, according to Behe, over and over again, his creation was woefully inadequate of facing the actual challenges that it would face, and so his all-powerful creator needs to constantly intervene, and tweak things in order to make them work. His God is a buffoon - a bumbling fool who isn't capable of creating worlds in a way that works."
I dont't know, what Behe has now written. But your logic sounds terrible:
If God is all-powerful, then he can do anything he wants to do. And then he could also use only some of his power in our universe if he wanted to. (And all-powerful agent could also make for example the world, where is not any life... or whatever.) So, even if God doesn't want to do something (and that's why "isn't capable" to do something), he can be, and is all-powerful.
You didn't made bad theology. Your "theology" was so bad, that it was not even theology. You made only an logical error.
Posted by: a | June 1, 2007 8:32 AM
"What's the favorite bullshit mathematical argument of creationist assholes worldwide?"
You lose reasonable civil people like me when you talk like this. Grow up for heavens sake.
I have NEVER seen Behe or any other well known IDer blog that someone is an "asshole" or that their arguments are "bullshit." You lose the majority of people when your argument is filled with such hateful attacks and the other side is actually, I don't know, CIVIL.
Posted by: Sanford Small | June 1, 2007 8:51 AM
a:
You're basically re-iterating my criticism of Behe as if Behe's reasoning were my invention...
*Behe* is the one who says that there is an all-powerful, all-knowing god who created the universe, created life, set it going down its evolutionary pathway, and then constantly had to tweak it, because it couldn't work properly on its own.
My point is that Behe's description of how life developed, and what God supposedly did to prod it along is incompatible with his description of God.
If there's an omniscient god, and he created the universe with the intention of creating life, then creating it in such a way that he needed to constantly intervene to make a tweak here, a change there, a nudge somewhere else - is the sign of an utterly incompetent creator.
As I've mentioned before, I'm a religious Jew, and I do believe in God. But I *don't* believe in the sloppy interventionist god that Behe describes. The concept of an all-knowing, all-powerful being that created the universe and the bumbling idiot of Behe's argument simply are not compatible.
Posted by: Mark C. Chu-Carroll | June 1, 2007 9:52 AM
Why dont you Google 'Dembskis Christmas Present' from 2006. That was fun.
'Asshole' is the nicest possible descriptor I can think of for Professional Creationists. If you dont understand why, then maybe you need to spend some time on Google and see if you can figure out why people some people might be a little angry with Creationists behaviors.
Posted by: ERV | June 1, 2007 10:05 AM
Would that be anything like the likelihood that Homo sapiens achieved a mutation that confers resistance to malaria, Dr. Behe? Or several such mutations in at least five different genes?
Malaria is an incredibly stupid example to use if you want to demonstrate the impossibility of resistance mutations in humans. Does Behe discuss the sickle cell trait anywhere in the book? I bet he thinks it doesn't count since it "does not add information to the genome" or something.
Posted by: windy | June 1, 2007 10:06 AM
Sanford:
http://rockstarramblings.blogspot.com/2006/11/doggerel-44-youre-just-rude.html
So, one sentence of my review was rude. I think it was appropriately rude. Behe and friends constantly trot out the same old nonsense, over and over, ignoring all criticism of it, and constantly presenting it as the unrefutable truth.
I'm particularly annoyed at the big-numbers argument, which I've written about lots of times before. It's the argument where you pull a bunch of numbers out of the air, multiply them together, and say "Look how big that number is!", as if proves anything.
That's exactly what Behe does. He comes up with completely unsupportable nonsense numbers, multiplies them together, asserts that they're a meaningful probability, and then says that probability is so large that it means it's impossible.
It's a crap argument, and the thing is, Behe *knows* it's a crap argument. He just doesn't *care* that he's reciting crap.
Calling him on it, and saying that it's bullshit, and that *he knows* it bullshit is perfectly valid. You might not like the words, but this isn't a debate about who writes prettier words, or who's more polite, or who's the nicer person. Behe would likely win *all* of those. But what we're talking about is math, science, and facts - and Behe loses on all of those. And writing style and politeness have zip-all to do with that. He's wrong, and he *knows* he's wrong.
Posted by: Mark C. Chu-Carroll | June 1, 2007 10:07 AM
Mark C. Chu-Carroll:
"You're basically re-iterating my criticism of Behe as if Behe's reasoning were my invention..."
No.
"My point is that Behe's description of how life developed, and what God supposedly did to prod it along is incompatible with his description of God."
If there is an omnipotent God, He could do anything. And He could also decide, how He uses His power. If He were omnipotent, he could for example decide to use only some of his power (and thus reject some of his power) in our universe, if He wanted.
That's why I can't understand, how Behe's position couldn't be compatible with the idea about omnipotent God. And that's why I see your claim as a logical error:
because all-powerful agent (by definition) could do anything - even to reject his power or to work like an "idiot", (if He wanted)...
Posted by: a | June 1, 2007 10:13 AM
Mark- I will assume that Behe doesn't make arguments he KNOWS are wrong ("crap" as you called it). That's just silly.
Is it possible he's right and you're wrong? Of course it is.
I read the link you posted. You're a 'skeptic', then? I assume that is the case, as you linked to the post defending the behavior of skeptics.
Civil behavior IS important. Civil people won't ever take your side arguing like this.
Posted by: Sanford | June 1, 2007 10:15 AM
Behe: "This continues the venerable Darwinian tradition of making grandiose claims based on piddling results."
Dembski: "...it's not ID's task to match your pathetic level of detail in telling mechanistic stories."
Such gentlemen. But at least they didn't use any naughty words!
Posted by: windy | June 1, 2007 10:17 AM
ERV- to argue there's danger in a creationist argument is absurd.
The great majority of Americans don't buy your side of the argument. I see no damage done. The world has yet to crumble. The earth hasn't stopped rotating.
Scare tactics don't impress me much.
You think there's some danger in their arguments, so that makes it okay to use vulgar terms and call names? Really mature.
Posted by: Sanford | June 1, 2007 10:18 AM
Windy- you're comparing apples and wrenches.
Behe described results not a person. Dembski called something pathetic. How you compare that to the sentence Mark used, I have no clue.
The point is- you will never win in the public arena as long as your rhetoric is so hateful. Adults make arguments without calling their opponents "assholes."
Posted by: Sanford | June 1, 2007 10:22 AM
Sanford wrote: "Windy- you're comparing apples and wrenches.
Behe described results not a person. Dembski called something pathetic. How you compare that to the sentence Mark used, I have no clue."
Actually, Sanford, he was referring to your statement that "I have NEVER seen Behe or any other well known IDer blog ... that their arguments are "bullshit." You're ignoring your own previous statements to try and make a specious point.
What's with all this concern about the word 'asshole' anyway? I haven't run into anyone in the past decade who hasn't used the word in public, including my ultra-conservative mother, father, sister, and 85-year-old grandmother. I'm guessing this is a red herring on your part, to try and draw the argument away from Behe's indefensible 'bullshit' arguments and into a discussion of civility. I've noticed that you have no defense of Behe's work.
This sort of double standard has been a constant force in the conservative and right-religious world for years. Dick Cheney can tell a congressman to 'go fuck himself' on the Senate floor and be applauded for it, while Harry Reid can't refer to Bush as a 'loser' without conservatives everywhere swooning and fainting in horror. Religious nutjobs can refer to scientists as 'deluded fools' without any justification or empirical argument whatsoever, but call a person an 'asshole' for such a statement and the nutjobs get all wide-eyed.
Sorry, shock at the use of naughty words went out of style when the PG-13 rating came in. People who ignore the bulk of an argument because of the use of one or two profanities are either being utterly dishonest or irrational.
Posted by: gg | June 1, 2007 11:00 AM
Sanford,
I agree, creationists never use cheap and possibly offensive rhetorical phrases. Next thing you know, somebody will be alleging that creationists have been tying in evolutionists with nazism.
Posted by: SteveF | June 1, 2007 11:28 AM
It strikes me that Behe's confusion is even more intense than let on here. Here can use a smooth fitness landscape if he wishes, but this matters little since, even with point mutations, he has to be talking about discrete changes in the fitness functon, not "infinitesimal" ones. Of course, one can, for convenientce, model the process as one of continuus change, i.e., as the evolution of a differential equatiion of some sort, and this may be pictorially helpful, but only at the expenxe of scarcificin key realism, which is vital as it happens for the points at issue. One needs as sell a basic grounding in multivariable critical point theory--Morse theory, if you will, in order to "classify" the fiefferent types of equilibria, stable and metastable alike. One must be able to switch to local coordinates without getting hopelessly confused as to the global picture.
Finally, there are vital matters of scale here, which Behe seems utterly at sea about. Every mutation is, to a degree saltational; what is key is whether that saltation improves fitness, or decreases it. and whether the change puts the fitness point in the basin of attractiion of an entirely different local extreme. This is clearly a matter of geometry and scale and classification of possible directions.and can't be decreed by fiat a priori--its an empiriical matter. A genome whose fitness is poiosed on a knifeedge can improve itself slightly by a small step in a particular direction; a small step in another direction will carry it precipitously downhill and thus, presumably, to extinction. The key is not the size of the step but the roughness of the landsape.
Speaking of which, there's nothing in this kind of analysis that requires a smooth landscape with smooth fitness functin. A continuous landscape with continuus, or even piecewise-continuous fintess functon works just as well, with, perhaps, a bit more realism.
Posted by: Norman Levitt | June 1, 2007 11:29 AM
Norman:
You're exactly right. The problem with Behe is that he's invoking a particular model of evolution as a search over the fitness landscape; and that he's relying in specific properties of the landscape and the search process - things like the shape of the landscape, the ratio of the size of possible changes relative to the sizes of the peaks of maxima, among others - but *without* ever making the case for *why* those properties have any relation to reality.
This goes back to something I've written about before. Mathematical modeling is a great thing: it's an incredibly useful technique, and personally, I find mathematical models of real phenomena to be absolutely fascinating. But to move from experiments/observations/analyses of mathematical models to predictions or statements about the real world, you need to *validate* that model, and show that it's an accurate reflection of reality. Behe never even *pretends* to take that step. He merely asserts that the landscape is a valid model, never explicitly states his assumptions about that model, never even runs and experiments in the model, never tests how well his model matches real observations, and then argues that the conclusions that he draws on the basis of his model are valid conclusions about reality.
The biggest condemnation of Behe's argument is the *observations* of evolution: the numerous cases where we can witness that things that Behe's model says are impossible can occur in reality.
Posted by: Mark C. Chu-Carroll | June 1, 2007 11:43 AM
a said: "If there is an omnipotent God, He could do anything. And He could also decide, how He uses His power. If He were omnipotent, he could for example decide to use only some of his power (and thus reject some of his power) in our universe, if He wanted.
"That's why I can't understand, how Behe's position couldn't be compatible with the idea about omnipotent God."
The problem with your argument, a, is that it fits with absolutely any result. Behe's position is compatible with an omnipotent God who chooses to use only part of his power in order make a Creation that needs constant tinkering. Mark's position is compatible with an omnipotent God who chooses to allow his Creation to evolve in accordance with the principles of mutation (a/k/a "variation") and selection first systematically discussed by Darwin.
Since belief in an omnipotent God who can choose to do or not do absolutely anything doesn't make either evolution or the arguments against it any more or less likely, perhaps you'll agree we should turn to the scientific research being carried on every day by good, smart, sincere people in order to find out just what God *did* choose to do? Good, then the answer is that He chose to let Creation evolve.
Posted by: Jud | June 1, 2007 12:01 PM
Sanford -
You haven't looked very hard.
did
Posted by: did | June 1, 2007 12:07 PM
Sanford has a point, which he's proven quite effectively by posting over and over again about your shocking (tsk tsk!) language, and completely ignoring the substance of your review. Why give the creationists ammunition by using language they can endlessly drag around as a red herring? The last paragraph of your review was far more effective criticism. Professors get called asshole routinely, at least behind their backs-- but wondering how the guy got tenure? Not one naughty word, but unless Behe's completely out of touch with reality, that had to have stung.
Posted by: hoary puccoon | June 1, 2007 12:32 PM
Behe got tenure because he waited until he got tenure before turning into a whackjob. Contrast that with Prof. Gonazlez who turned into a whackjob before getting tenure.
Posted by: SLC | June 1, 2007 1:08 PM
Well, Sandford, if your oh-so-delicate sensibilities cannot tolerate being near a naughty word (like Ming vases, Creationists), youre more than welcome to look at my post, or any of the ones Blake Stacey collected to learn about Behes difficulties in the subjects he professes to have mastered.
Can you do that, Sanford, or would you rather troll here as an attention whore?
Or do you have nothing to contribute to this conversation besides being a cry baby?
Posted by: ERV | June 1, 2007 1:19 PM
Of course it could be. Indeed, there is absolutely nothing that is incompatible with the idea of an omnipotent, sufficiently capricious God, including the idea that the universe was created 5 minutes ago, fossils, memories, and all. That's one reason why scientists reject the notion of ID as science, because it refuses to hypothesize as to the nature of the supposed Designer, which renders the theory completely untestable.
On the other hand, from a theological point of view, I can easily see why many people find the notion of a capricious, arbitrary God unsatisfying. If God is intelligent enough to create a universe that fulfills His will simply by virtue of its fundamental nature, why would he keep tweaking it? Are we to conceptualize Him as some sort of cosmic hobbiest, rerouting the model trains for His own Personal amusement? If he can make a real thumb, why not give the panda one, too? Is this His idea of a joke? One tends to expect a higher standard of behavior for God.
Posted by: trrll | June 1, 2007 2:20 PM
In my experience, the sort of people who nitpick about rude language will always find something trivial to complain about as an excuse for ignoring substance. If it's not language, it will be spelling or grammar.
Posted by: trrll | June 1, 2007 2:28 PM