My husband, mother, father, myself, and my four-year-old son were going out for a walk. It was raining. My son refused (as usual) to wear his raincoat. Instead, he carried a cup, which he held out in front of him. He argued that he was going to catch the rain drops in the cup so that by the time he got to the place the raindrops had been, they’d be in the cup and he’d be dry. Half an hour later, four adults were still standing around, drawing diagrams on the backs of envelopes, arguing about Pythagoras and trigonometry, all to no avail. We went out, with cup, sans rain coat. My son got wet. He insisted he remained dry.
Bryce Canyon, Utah.
I’ve got as far as Chapter 5 of Dembski’s book No Free Lunch, the chapter called Evolutionary Algorithms, and about which he says in his Preface: “This chapter is the climax of the book”. He claims that in it he shows that “An elementary combinatorial analysis shows that evolutionary algorithms can no more generate specified complexity than can five letters fill ten mailboxes.”
I think he’s making the same kind of error as my son made.
Many people, including people with far more mathematical expertise than I (including real mathematicians) have had a go at Dembski’s NFL arguments, but I’m going wade in anyway.
What I do like about Dembski’s writing is that he commits himself to clear operational definitions. He defines “evolutionary algorithms” as “any well-defined mathematical procedure that generates contingency via some chance process and then sifts it via some law-like process.” It’s a shame that he is so hyperfocussed on Dawkins’ Weasel, which is a highly atypical example of evolutionary algorithms, and differs from those postulated to be applicable to biology on many important ways, but I’ll start there anyway
The first confusion (apart from the latching issue,which I’ll ignore) that I think Dembski introduces is on page 188 in my edition, where he is describing “phase space”, the “space” of all possible strings of given length (28 in the case of Weasel, 500 in my own example) consisting of an alphabet of given size (26 letters +space in Weasel; Heads and Tails in mine):
If you think of the phase space as a giant (but not infinite) plane…
On the previous page, Dembski says:
The univalent measure defined with reference to theh pahse space an dneeding to be optimized is known as the fitness function (also fitness measure or fitness landscape).
implying that these three terms are interchangeable. This is important, because if “fitness landscape” means the same as “fitness function” it would imply a fitness topography that is independent of the topology of “phase space”.
On the topology of “phase space”, he writes
…(1) any point in phase space has zero distance from itself; (2) the distance between two points does not depend on the order in which one considers them (e.g. flying from Atlanta to Dallas is the same asdistance as flying from Dallas to Atlanta); and (3) the direct distance between two points is never bigger than the distance of going through some intermediate point.
However, if we are talking about every possible linear sequence of N characters drawn from an alphabet of M letters, there is more to the topology of phase space than that, and “plane” seems to me a misleading image. I’m going use my example, to explain what I mean, rather than Weasel, because it’s simpler (only two “letters” in its “alphabet”, namely Heads and Tails).
Let’s (imaginatively) plot every possible sequence of Heads and Tails in a 500 coin-toss series (i.e. 2500 possible sequences) on the surface of a globe. First we put 500 Heads at the North Pole and 500 Tails at the South Pole. Going to the South pole, and heading North, we will first of all meet a latitude in which all the sequences have 499 Tails and one Heads, and there will be 500 of these, each with the single Heads at a different position. Heading North again, we will next meet a latitude in which all the sequences have 488 Heads and two Tails, and so on. All sequences with 250 Heads and 250 Tails will be systematically arranged around the equator.
Now if we regard each sequence as being at a node on a graph, and connect with a line (an “edge”) all points that only differ at one position, we will find that at the sequence at the South Pole is connected to every node (500 sequences) in the latitude immediately to the north of it, and each of these nodes in turn are connected to 499 of the (500*499) nodes at the latitude one step more northerly still, and so on. This means that we can travel from every node to every other node by a series of “edges”. If we want to travel from the South Pole to the North Pole, we can do so by any one of a vast number of routes, the shortest of which will use steps that are always to a more northerly latitude. In mutation terms, this means that each all points in each latitude is a single point mutation away from many points on the next more northerly or southerly latitude.
We also use a “spring embedding” algorithm in order to arrange the nodes at each latitude in a way that physically minimises the length of each edge. This will make it easier to envisage the shortest routes between any pair of nodes.
So that is how I am envisaging the topology of phase space – as nodes on a globe all of which are connected by a single point mutation to at least 500 other nodes,
So what about the Fitness Function/Landscape? In Weasel this is dead easy, and the equivalent in my example would be simply specifying a target sequence and a starting location. Let’s say I choose as my target sequence, the sequence at the North Pole (500 Heads) and I make life as difficult for my Traveller as possible by starting at the South Pole (500 Tails). Now, for this target, my fitness function can simply be the sum of Heads (as in Weasel – the sum of letters in the correct position). But what of the fitness landscape? The topography?
If we imaginatively represent the sums of Heads (i.e. the fitness function) for each node as shades of grey, in which all-Tails is white, and all-Heads is black, then when we look at our globe, we will see a white South Pole, a black North Pole, and a mid grey equator, with all other latitudes smoothly graded in between. Or, if we liked, we could represent the fitness function as metres below sea level, and simply let our Traveller (let’s put her on a skate-board) roll straight downhill from South to North (hence the terms “landscape” and “topography”).
We could make it more difficult by making the target sequence some sequence on the equator, and the starting sequence some randomly chosen node anywhere on the globe. Now the fitness function cannot simply be “sums of heads”. This time we have to sum the number of positions in each sequence that are shared with the target sequence. Now the dark or deep nodes (high fitness) will be clustered around the target-sequence in a roundish dark patch extending north-south as well as east and west from the target. And again, there will be a smooth gradation of grey over the globe, and a smooth downhill run from any point on the globe towards the target.
And, as Dembski justifiably says, this is cheating. At one level it’s cheating because we’ve specified the target in the fitness function (the “information” has been “smuggled in”) as a specific sequence against which intermediate sequences are evaluated. At a more important level, it’s cheating because we’ve designed the fitness function so that when applied to the phase-space topology there is a straight down hill run to the target.
But what I want to show is that it is perfectly possible to a) specify the target in the fitness function, and NOT have the evolutionary algorithm find it, and b) not specifiy the target in the fitness function and STILL have the evolutionary algorithm find it. The issue, in other words, I would argue, is not whether you specify the target in the fitness function, but the topography of the fitness landscape, which is, in turn, a function of the topology of the phase space – the very aspect of its topology that Dembski ignores.
To take a) first. Let’s suppose that the target is some sequence with approximately equal ones and zeros (perhaps a Shakespearean phrase rendered in Morse, with runs-of-heads equal to sound and runs-of-tails equal to silence). Using our old phase space, this target will be a dark patch somewhere on the globe representing a low point to which all things tend to fall.
However, let’s change the mutation system. This time, instead of single point mutations, the only mutations allowed will be single change-of-place mutations (the value H/T at place i trades with the value H/T at place j). If we now reconnect our nodes that are one-mutation away from each other, and reapply the spring-embedding, we will have something quite different from the single-point-mutation plotting. Our poles will be completely disconnected from the rest of the globe and from each other, and worse, all latitudes will be disconnected from each other as well. Worse still, what was a nice focussed dark patch representing our Shakespearean phrase in Morse will be a scattered mess of dark spots. This means that even if, by chance, you start at the same latitude as the target, there won’t be a nice straight downhill ride towards it, but a roller-coaster. In other words, there is a very small probability that a series of mutations, even if selected for their similarity to the target (in terms of how many locations in the string have a value shared with the target) will actually get there. The target, despite being specifically encoded within the fitness function, is now Irreducibly Complex. That doesn’t mean it can’t be found, but the probability is far lower than it would be when situated within a smooth fitness landscape.
And this is why fitness landscape and fitness function are not, contra Dembski, the same thing.
To take the second scenario, b: this time the target is as in my exercise: it’s a subset of phase space, not a single target, but the subset has been chosen to be of a size that means that, according to Dembski’s paper: Specification: the Pattern that Signifies Intelligence, it has Specified Complexity (i.e. it’s a very small subset of the whole of phase space). In other words there are several nodes on the globe that are near-black (have the target fitness), and all other nodes are shades of grey. If we take our first mutation type (the one in which the edges connected of single point mutations), it turns out that the black target nodes are in northern temperate latitudes (more Heads than Tails), but rather more scattered as to longitude, although still clustered. However, although scattered, the whole cluster is fairly dark grey, and viewed from a distance, there is a definite east-west dark stripe with shades of grey elsewhere varying from white at the South Pole, as before, mid grey at the North Pole, at the Equator, and so on. So while the odds of the traveller rolling into the very blackest hole are fairly small, the odds of it rolling into a supra-threshold dark hole are really quite large.
Yet none of these holes are specified in the Fitness Function – what is specified is the properties that the sequence must have, not the sequence itself.
And we can increase the probability that the traveller will roll into a dark hole still further by adding mutation types (and thus more edges), or increasing (up to a point) the likely number of mutations in a single iteration. All these will increase the connectivity between nodes, and increase the probability that there will be a downhill path (via the edges) from the starting node to one of the target nodes.
And if Dembski objects that I have still “smuggled in” information about the target sequence by specifying the properties it must have, I plead guilty, but respond that: All I have “smuggled in” is the problem to be solved. I have no more “smuggled in” the solution(s) to the problem than an examiner “smuggles in” the answers on a math exam in the guise of the questions asked. The fact that at least one solution exists is neither here nor there. If I had “set” an impossible problem (one to which there is no solution), no algorithm is going to find a solution, clearly. The reason we use evolutionary algorithms practically is not so that we can print a phrase of Shakespeare we already know, but to find a solution we don’t know to a problem we want to solve. To gain information.
So Dembski, it seems to me, has conflated fitness function with fitness landscape, and, rather like my son, as a result, failed to note that the fitness landscape is in part a function of an aspect of phase space topology he hasn’t even considered (how the elements of phase space are connected in any given physical system). And, presumably as a result of that, has failed to note that while it may be true that averaged across all possible fitness landscapes (including those in which the dot-shades are uniformly scattered across the globe, giving a landscape rather like Bryce Canyon, pictured above, and of those, those in which all dots are either white or black, or all dots bar one are white – a uniform surface with a single deep well), evolutionary algorithms fare no better than “random search” (as the NFL theorems state), there are many naturally occurring fitness landscapes, including those in biology, where phase space has the kind of highly interconnected topology (many sequences one step apart) that will tend to make “problem space” (the fitness landscape) for many fitness functions relatively smooth, and thus the finding of a solution to a target problem fairly tractable for evolutionary algorithms.
Including solutions that have “specified complexity” of chi>1 and are therefore in Dembski’s rejection region for non-design.
Again, if you design something, an algorithm, to solve a problem, and it does, then it did so by design.
And with biology whatever survives to reproduce, survives to reproduce.
Yes.
But I’m not sure what the relevance of your comment to what I wrote above is.
Physical scientists (and biological scientists too) use lots of very intelligently-deisgned models. For example, really clever fluid-dynamic models used to predict weather. And that is not an argument that the weather is changing from hour to hour because of the intervention of a Higher Intelligence. In fact, the models are intelligently designed to explain the weather only by nonintelligent processes of fluid dynamics and heat flow. So pointing out the intelligence of the researcher is no argument whatsoever.
Elizabeth, I agree with your post. In my 2007 article, I cited about 7 people who had made this criticism of Dembski’s No Free Lunch argument, starting with Richard Wein and with Jason Rosenhouse in 2002.
I think that Dembski regards his Search For A Search argument as the rejoinder to his. Only a tiny fraction of all possible fitness surfaces are smooth enough to let evolution by natural selection work. He would regard the very ability of natural selection to succeed as evidence that a Designer chose the fitness surface out of all possible ones.
There are two problems with that:
1. He is then backing away from his claims that natural selection cannot work to improve adaptation. In the Search For A Search argument the Designer is working only at the start, and then leaving evolution to do the rest. Most biologists would call a process Intelligent Design only if the Designer intervenes at least once after the start.
2. Physical processes, that have influences dying away by inverse-square laws, may be sufficient to explain why the fitness surface is not infinitely jaggy. In a fitness surface randomly chosen from among all possible fitness surfaces, one change of one base in the DNA takes us to a fitness that is horrible. In fact, to one that is just as bad as changing all bases simultaneously! Real biology does not work that way, and I think this is because real physics does not work that way.
Yeah, Dembski effectively gives up the fight for evolutionary biology. I am sure his
creationist friendsIntelligent Design colleagues are thrilled.I’m afraid there is a third problem: The mathematics of his paper “A Search for a Search” aren’t sound. A couple of days ago, I wrote up a simple refutation of one of the main points in his paper: Have a look, shouldn’t take long….
I’m afraid I’m lost on all this search for a target.
It seems to me that evolution proceeds by replacing a string by a nearly identical string. The “target” is any minimally different string that is not severely detrimental.
An evolutionary algorithm is not searching for anything specific and is certainly not searching for anything that is distant from any given starting point.
For an IDist who regularly says that ID isn’t anti-evolution, you sure are anti-evolution.
I agree that it is a really bad image. That’s why I prefer the mental image of things rolling downhill – or of “attactor basins” anyway.
Once you have the prerequisites for Darwinian evolution (things self-replicating with variance in an environment in which some variants reproduce better than others), you will have a virtual “network” of variants that are similar (are a few mutations apart, how many depending on what kinds of mutations are intrinsic to the variance-producing mechanisms, i.e. the biochemistry), and if some areas of this “network” are more conducive to reproduction, the populations will tend to “roll into them”. The aren’t “searching” for the low places, that’s just where they end up.
And if variants that are similar genetically also tend to be similar phenotypically, and if similar genomes are reachable by common mutation-types, then the topography of the fitness landscape will tend to be smooth.
So there isn’t a problem. “Blind” search is just fine, because those “blind” populations will find their way to the basins just as “blind” raindrops find their way to the seas, if they don’t dry out on the way.
Elizabeth wrote
Bingo!!
petrushka wrote
As I have said many times, starting years ago on Infidels, the search metaphor for biological evolution is a snare and a deception. Evolution doesn’t “search.” It finds, but as a by-product of the operation of the (very simple) evolutionary algorithm. It finds adaptive solutions (or not, in which case extinction follows) without searching for them.
And once again- if you need to start with replicators then you don’t know if you have darwinian evolution, front-loaded evolution or intelligent design evolution.
Also there isn’t any evidence that some simple self-replicator, which you cannot show ever existed, can evolve into a living organism- no connection in any search space.
1- How can “evolution” find something that doesn’t exist?
2- What evolutionary algorithm are you talking about?
This is just Joe G making his claim that Dembski’s CSI argument is only supposed to be applied to the Origin OI Life. He and I have been back and forth on this. Not only has he failed to convince me, he has failed to convince any of the other people here who have read Dembski, including any of the other ID proponents here. He is all alone in that.
For the full flavor of Joe G’s subtle wisdom on this, interested readers should see the discussion of this at his own blog Intelligent Reasoning.
With respect to biology CSI pertains to its origins, and I have supported that claim. Just because you are not convinced doesn’t mean anything to reality.
Then you should be eager to demonstrate the origin of CSI in biological things, and the origin of the originator (aka “the designer”) that the CSI originally came from. Will you?
Is “the designer” biological?
Hey Elizabeth-
You say you are reading “No Free Lunch”- do you now understand that CSI pertains to origins? Chapter 3 takes care of that.
I’m sure CSI pertains to origins. But we can’t compute it for OOL, because we don’t know how simple the simplest Darwinian-capable self-replicator was.
So we can’t tell whether chi>1.
What would you say if, instead of “adaptive solutions”, the wording were changed to ‘stochastic adaptive results’, or to ‘survivability and reproduction’, or to ‘results that allow survival and reproduction’, or to ‘results that enhance survival and reproduction’, or to ‘results that sometimes enhance survival and reproduction’, or to ‘survival and reproduction for the organisms that fit best with their environment at the time’?
Some posts moved to the new Sandbox.
Trying to keep this thread fairly focussed….
Dr. Liddle,
Since you are a neuroscientist, the topic of specified complexity is subject to some psychological experiments.
When I taught ID at informal gatherings at James Madison University I got the students to form small teams. I gave the teams boxes and several dice and several coins. Each box had the same number of dice and coins. I selected one student to be my assistant. I and my assistant then turned our backs.
The teams were instructed to randomly shake one box and then build designs of their choosing in the other box. I enccouraged them to be creative. After they were done, I and my assistant then went to each team. Without failure we were able to detect which box contained a design even though we had never seen the design before in our life.
The experiment has obvious lack of rigor, but nothing that can’t be fixed with some determination.
They were building structures that evidenced specified complexity.
If we tied a robot to an evolutionary algorithm that would feed the robot instructions on how to orient and position the dice and coins in the box such that it evidences specified complexity, the evolutionary algorithm will only be able to converge on such solutions if it is programmed with sufficient information.
We can certainly build robots that can make structures that looked designed (that’s pretty much what factories do), but they cannot do so in a blind manner. Even in watch factories, watchmakers aren’t really blind. Most factory feedback/control systems (akin to evolutionary alorithms) must be tuned by a designer to make designed products, othewise it results in disaster.
What is lost upon many scientists is that Evolutionary Algorithms in nature often select against design. Allen Orr when arguing agasint Dennett said “selection doesn’t trade in the currency of design”. He then went on to describe how natural selection favored blindness over sign in Gammarus Minus, thus selection in nature tends to destroy design, not make it. The same is true in the evolution of anti-biotic resistance, all cases of anti-biotic resistance can be described as loss of integrated complexity not increase of it.
Thus we have empirical evidence, that in nature, the evolutionary algorithms in the natural world do not, as general rule, work to increase integrated complexity but often will select against it.
What NFL argues is the level of design needed in an Evolutionary Algorithm to be able to arrive at designed object like:
1. the dice and coin configurations in the students boxes
2. products of factories
3. biological systems
etc.
The question arises why are humans wired to see certain configurations of matter as desgined and others as not designed? Can biological evolution explain why things looked designed? Is the propensity to think certain objects look designed the product natural selection? But that is not the end of the story.
It is a two-proned problem:
1. will NS create brains that are able to recognize designs
2. will NS create objects that can be recognized by such brains
This is not far from the problem of matching passwords to login. Evolutionary Algorithms (or any algorithm for that matter) will not be able to solve logins and passwords without sufficient front loaded information. That is why GA can’t be used with much effect to solve the specified complexity of passwords (and that is a good thing).
The question of biological evolution is why we have brains that attribute design to some objects, and why such objects exist. If we look at our brains as the receiver of information and the objects as the transmitter of information, will the process of natural selection or chance or other things in nature provide an adequate explanation for this coincidence. The problem does not seem to be solvable with appeals only to physics and chemistry (the basis of much of our science).
And FWIW, I would argue that physics, chemistry, and empirical observation actually conflict with Darwin’s notions of Natural Selection and against the portrayal of Genetic Algorithms as the means of biological evolution, but that is another story.
That doesn’t surprise me in the least 🙂 And the experimental methodology seems just fine to me.
I would expect the results from box shaking to be detectably different from the results from human beings encouraged to be creative with the contents of the box, just as I would expect the result from drawing scrabble letters from a bag and setting them down in the order of the draw, from the results of drawing the same letters and asking human beings to arrange them in some kind of interesting order.
Well, it needs to be programmed as an evolutionary algorithm, obviously! Which would entail some kind of fitness criterion. What did you have in mind?
Of course.
Please explain exactly what you mean by this.
What is “integrated complexity”? And can you give a citation to the empirical evidence that supports this claim?
I’m not parsing this. Is there something missing?
Yes, I think so. Clearly being able to parse the world into firstly, events and objects, and secondly, into causal relationships between events and objects is likely to be advantageous to the organism, as is the capacity to infer intelligent agency. It also seems to be “hard-wired” in human beings. This has been shown in a number of interesting experiments with infants, in which cartoon objects, deliberately designed (heh) not to look like animals, nonetheless behave like intelligent agents, chasing each other and “trying” to do things to each other. Infants can distinguish between “intentional” behavour on the part of these objects, and non-intentional behaviour. They also distinguish between protective and agressive behaviour. Even though the objects are just triangles and squares, moving around the screen.
I don’t see why not. As long as by “NS” you refer to the whole evolutionary algorithm, namely self-replication with heritable variance in reproductive success in the current environment, i.e. the variance-generation part as well as the proviso that different variants have different probabilities of reproductive success in the current environment.
Indeed. Passwords are designed (that word again) to be unfindable by evolutionary algorithms, i.e. they exist in unconnected search space.
Biological features exist in connected search space.
Well, I think it is a somewhat ill-posed question (objects don’t really “transmit” information in most senses of the word “transmit” or “information”) but even if we gussied it up a bit, I don’t see why it’s not solvable.
Well, if you would like to write an OP, I’d be delighted 🙂 I’ll give you posting permissions.
Dr. Liddle,
I would be honored to write an OP or a few OP. The rigor of Bill Dembski’s work, like most mathematical works, tends to cloud some of the more straight forward insights that are easily perceived.
I’m trying to vet some of my material as I’m teaming up with ID friendly biologists and chemists and computer scientists to put together a course on creation and evolution to be taught in religion departments of Universities. People hostile to ID have told me they have no objections to ID being discussed in religion classes at US universities, and even Eugenie Scott expressed support for the idea. This is already happening in some US secular classrooms, but the teaching materials are extremely wanting, and sometimes needlessly complicated.
I was hoping participation in this forum would help improve what I wrote. Even if it might not be convicing to the majority of the scientific community, I wanted to expose some of my ideas to criticism in the hopes of improving them, at least in terms of clarity. If people disagree with the ideas, I would at least hope they have a clear perspective of what they are actually disagreeing with. That’s about the most I could hope for.
I am familiar with how some of the posting mechanics might work. I can write an OP regarding this topic. I’ll try to do a good job for your website.
Thank you.
Sal
(aka stcordova, aka scordova at Uncommon Descent)