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Author
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Topic: Weak No Free Lunch vs Strong No Free Lunch
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Iain Strachan
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Member # 96
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posted 08. May 2002 19:08
Many critics of Dembski's use of the "No Free Lunch" theorems take issue with it by pointing out that these theorems are based on averaging over all possible fitness landscapes, the vast majority of which are completely irrelevant, and
represent problems that are not interesting to solve, because the fitness landscape looks like a random array of spikes.
I would have to say that I also share this worry. I was aware of the No Free Lunch theorems long before I was aware that Dembski had written a book with the same name and I initially wondered if this might provide a theoretical underpinning to the idea that design cannot be achieved without intelligent input. But then precisely
the same objection occurred to me (that the generality of the result severely limited its relevance to practical problem solving), and I felt that one should be cautious in citing
the NFL theorems to justify the design hypothesis.
It may be that I have misunderstood Dembski's argument, and I would certainly like to see him respond to this criticism.
However, rather than make this a purely negative criticism, I would like to offer what I propose to call the "Weak No Free Lunch principle" as an alternative insight. This is based, not on a mathematical theorem, but just on practical experience from many years working in the field of Neural Networks, and (occasionally) genetic algorithms. In order to achieve a satisfactory result in training a Neural Network, it is almost always essential to perform intelligent preprocessing of the data, and to exploit one's problem-specific knowledge of the nature of the data set being analysed. The same principle applies to the design of genetic algorithms. Dembski states that this knowledge is embedded in the design of the fitness function, but in practice, it is also in the design of the mapping
from Genotype to Phenotype; where on the genome to place certain quantities, what type
of selection procedure to adopt and so forth. It's generally the case that you don't
get out more than you put in (i.e. you don't get a free lunch). Your Neural Net will not
in general extrapolate beyond the range of the training data (though it may be able to
interpolate - a property known as "generalization" - due to the fact that it is a curve-fitting procedure).
This I would call the "weak No Free Lunch" principle, because it describes the way we work
in practice, and it looks like an inevitable consequence of the NFL theorems, but I don't really think it is directly linked to them. Most of Dembski's arguments about the input of information "up front" into the algorithm apply equally well under this principle - the input of this information is simply standard accepted practice in machine-learning applications.
By contrast, the "Strong No Free Lunch" principle would state that NFL theorems prove that you have to insert intelligence at the front end, because, on average, a GA is no better than blind search or a hill-climber or whatever.
I personally think that "Weak" is stronger than "Strong" ![[Cool]](cool.gif) , but I would like to see Dembski address the above criticisms
of the "Strong" version - because perhaps there is some subtlety that I have missed.
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Erik
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Member # 160
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posted 09. May 2002 11:34
quote:
Iain Strachan: Many critics of Dembski's use of the "No Free Lunch" theorems take issue with it by pointing out that these theorems are based on averaging over all possible fitness landscapes, the vast majority of which are completely irrelevant, and represent problems that are not interesting to solve, because the fitness landscape looks like a random array of spikes.
Ironically, even if we grant that the prior over the set of all cost functions is uniform, the NFL theorem does not say that optimization is very difficult. It actually says that, when the prior is uniform, optimization is child's play! I mean that almost literally. Almost any strategy no matter how elaborate or crude will do. If the prior over the set of cost functions is uniform, then so is the prior over the set of cost values. That means that if we sample a point in the search space we are equally likely to get a low cost value as a high cost value. Suppose that there are Y possible cost values. Then the probability a sampled point will have one of the L lowest cost values is just
r = L / Y,
regardless of which strategy that was used to decide which point to sample. The probability s that at least one of N different sampled points will have a cost value among the L best is given by
s = 1 - (1 - r)^N,
again independently of the strategy used. Is that good or bad performance? The number of points required to achieve a given performance and confidence level is
N = ln(1 - s) / ln(1 - r) ~ - ln(1 - s) / r.
After sampling 298 points the probability that at least one of them is among the best 1% is 0.95. After 916 sampled points the same probability is 0.9999. If instead we want a point among the best 0.1% we need to sample 2994 points to find one with probability 0.95, or approximately 9206 points to find one with probability 0.9999. That kind of performance may not be satisfactory when the optimization must be done very fast in real-time under critical conditions, but it is good for most purposes. Certainly our universe would seem to be able to spare the time necessary to sample 9206 points. This is why Thomas English wrote
quote:
"The maligned uniform distribution is actually benign. The probability of finding one of the better points with n evaluations does not depend on the size of the domain [7]. For instance, 916 evaluations uncover with 99.99% certainty a point that is better than 99% of the domain. What is remarkable about NFL and the uniform is not just that simple enumeration of points is optimal, but that it is highly effective." (see below for a reference)
The inference is never better than the assumption of a uniform prior that it relies on, however. It would seem that in most non-trivial optimization problems the number of good points in the search space are not as frequent as the number of bad points, meaning that the corresponding cost functions are not drawn uniformly from the set of all possible cost functions.
quote:
Iain Strachan: I would have to say that I also share this worry. I was aware of the No Free Lunch theorems long before I was aware that Dembski had written a book with the same name and I initially wondered if this might provide a theoretical underpinning to the idea that design cannot be achieved without intelligent input. But then precisely the same objection occurred to me (that the generality of the result severely limited its relevance to practical problem solving), and I felt that one should be cautious in citing the NFL theorems to justify the design hypothesis.
In addition to the ironic assumption of a uniform prior, there is also the problem that Dembski has misunderstood the role of a cost/objective/fitness function in optimization. As I have pointed out in another thread, the cost function is the mathematical representation of the problem to be solved. It is part our definition of the mathematical problem, not, as Dembski seems to think, a part the attempt to solve it. Such conceptual mistakes deprive Dembski's argument of all its force.
quote:
Iain Strachan: However, rather than make this a purely negative criticism, I would like to offer what I propose to call the "Weak No Free Lunch principle" as an alternative insight. This is based, not on a mathematical theorem, but just on practical experience from many years working in the field of Neural Networks, and (occasionally) genetic algorithms. In order to achieve a satisfactory result in training a Neural Network, it is almost always essential to perform intelligent preprocessing of the data, and to exploit one's problem-specific knowledge of the nature of the data set being analysed. The same principle applies to the design of genetic algorithms. Dembski states that this knowledge is embedded in the design of the fitness function, but in practice, it is also in the design of the mapping from Genotype to Phenotype; where on the genome to place certain quantities, what type of selection procedure to adopt and so forth. It's generally the case that you don't get out more than you put in (i.e. you don't get a free lunch). Your Neural Net will not in general extrapolate beyond the range of the training data (though it may be able to interpolate - a property known as "generalization" - due to the fact that it is a curve-fitting procedure).
Although such an argument may have an intuitive appeal, I think that it makes little sense. You assert that we can't, in practice, get out more from a genetic algorithm than we put in. I reply with two questions: Exactly what is put into the genetic algorithm and exactly what does one get out? And how can we compare what is put into the genetic algorithm with what one gets out?
It must be kept in mind that neural nets and genetic algorithms are devices for solving certain kinds of mathematical problems. Of course, if you wish to attempt to solve a technological or economical problem using, say, a genetic algorithm you must first translate it into a mathematical problem. You must also find a way to execute the genetic algorithm (e.g. with a paper, pencil and a die, or on a computer). The solution generated by the genetic algorithm is then translated back from mathematical language to the technological or economical terms that originally defined the problem. Such work is irrelevant since it is of a very different kind than that done by the genetic algorithm. There is, however, a kind of relevant work: You sometimes can utilize your knowledge of the problem to choose a particular set of initial parameters and a representation that enables the genetic algorithm to solve it more quickly. You would then have solved part of the problem for the genetic algorithm. I suggest that we measure such work by the amount of run-time it saves. You may be able to reduce the run-time by 25%, or even 99%, but genetic algorithm would still do the remaining 75% (or 1%)--the part that you couldn't solve yourself--and there is no coherent sense in which you could say that you put in more than you got out.
quote:
Iain Strachan: This I would call the "weak No Free Lunch" principle, because it describes the way we work in practice, and it looks like an inevitable consequence of the NFL theorems, but I don't really think it is directly linked to them. Most of Dembski's arguments about the input of information "up front" into the algorithm apply equally well under this principle - the input of this information is simply standard accepted practice in machine-learning applications.
What do you mean by "information"?
It may interest you to know that a rigorous information-theoretic analysis of black-box optimization has been done. It is reported in the following article (which is also the source of the quote above):
English T. (1999) "Some Information Theoretic Results On Evolutionary Optimization", Proceedings of the 1999 Congress on Evolutionary Computation: CEC99, pp. 788-795
English shows that, in a certain sense, the sum of the Shannon entropy of the visited points in the search space and the unvisited points is constant. (I must point out that I mean "information-theoretic" in the standard sense of an analysis within Shannon's theory, not an analysis with Dembski's framework which he unfortunately also refers to as "information-theoretic".)
Erik
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John Bracht
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Member # 5
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posted 15. May 2002 22:58
Iain,
I've been doing some thinking about the NFL principles lately and wanted to respond to your thought-provoking thread.
I am probably just missing something, but I think there really is little or no difference between the "weak" vs "strong" NFL principles.
It is my understanding that the NFL principles simply state that, averaged over all possible fitness functions, no search algorithm is better than any other. In other words, there is no inherent "bias" towards any particular result. This just states what should be intuitively obvious: a state of complete randomness or uniformity (averaged over all fitness functions) gives no inherent bias toward any particular result.
Thus, in order for an algorithm to be able to target a particular solution, it has to be biased by the programmer toward that solution. The NFL theorems guarantee that the biasing cannot come from any inherent properties of the class of possible fitness functions (because averaged over all possible fitness function no particular solution is priviledged) so this bias must be provided entirely by the programmer's input: the fitness function and encoding and logic of the program. Indeed, the degree of biasing of the result is directly correlated with the degree of biasing of the input by the problem representation and fitness function. In giving the problem statement and setting up the program to solve it, we are essentially giving the program the answer it eventually outputs.
Geoffrey Miller of University College London, comments,
quote:
But for hard problems and very large design spaces, designing a good genetic algorithm is very, very difficult. All the expertise that human engineers would use in confronting a design problem--their knowledge base, engineering principles, analysis tools, invention heuristics and common sense--must be built into the genetic algorithm. Just as there is no general-purpose engineer, there is no general-purpose genetic algorithm.
(from: Miller G. Technological Evolution as Self-Fulfilling Prophecy. In: Ziman J, editor. p 208.)
In other words, the engineering is done by the human in setting up the program, not by the program in solving the problem.
Melanie Mitchell seems to tap into this intuition when she writes:
quote:
In fact, coming up with the best encoding is almost tantamount to solving the problem itself!
(from: Mitchell M. An Introduction to Genetic Algorithms. Cambridge: MIT Pr.; 1998. p158.)
I would go further to say that setting up the encoding (and the fitness function) is tantamount to solving the problem itself.
Furthermore, to the degree that evolution works in the real world, we are justified in being astonished. Kauffman comments with wonder on the fact that the world contains the fitness functions capable of producing the incredible biosphere. Where do these wonderful fitness functions, that enable evolution, come from? After all, a truly random fitness function won't help biological evolution any more than it would help a genetic algorithm. Somehow, smooth and finely-wrought fitness functions exist and this allows evolution to happen. The NFL principles allow us to realize that we cannot just accept the fitness functions as "given"--they are not helpful when averaged over the whole set, so somehow the "right" ones have been chosen from this set. This is how Kauffman uses the NFL principle in his latest book Investigations. To explain the origin of these smooth fitness functions, Kauffman posits that they somehow co-evolve with the organisms that exploit them in a self-organizing process. In my opinion, he's just being vague enough to be able to shift the cause from organism to fitness function or vice versa, whenever anyone tries to pin him down to a real explanation. When asked where the organisms come from, he points to the fitness function, but when asked where the fitness functions came from, he points to the organisms that co-evolved with them. This is a non-explanation. One or the other has to be the source that directs the evolution; they can't just emerge together from nothing.
In other words, we can't just take the problem encoding and fitness function for granted. They don't just pop out of thin air, and they constitute an example of specified information that is being injected into the system and are required before any evolutionary process can even get started.
Just a caveat: I'm not referring to a fine-tuning argument as Richard Wein takes it. He points to the uniformity of natural laws as being the source of uniformity of the fitness functions in biological evolution. However, as Dembski points out, biological fitness functions are completely separate from natural laws and have to do rather with biofunctionality and issues like protein folding. These "biofunction" fitness functions are often highly irregular and map onto a higher order space that is consistent with natural laws but not merely reducible to them.
There's another aspect to Dembski's argument as I understand it: The Darwinian fitness function doesn't target some biological structures (like the bacterial flagellum or other irreducibly complex structures). In other words, there is no "bias" in the fitness function that produces these structures (because no gradual improvement leads to them). This means that the production of these systems cannot be explained by the Darwinian mechanism.
I don't know if this clarifies or not, but I think the important point about NFL is that the problem statement and parameters (including the fitness function and encoding) are themselves instances of design that contain all the information outputted by the algorithm or evolutionary process. This means that as far as an evolutionary process works, it does so due to its well-crafted fitness function--a function that itself needs explaining. Averaged over all fitness functions none of them are biased toward any particular result; the selection of the relevant and useful fitness function is an instance of teleological input. I think this argument subsumes both the strong and weak NFL principles Iain described.
John Bracht
[ 16 May 2002, 00:43: Message edited by: John Bracht ]
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Jesse
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Member # 112
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posted 16. May 2002 17:02
I think we need two distinguish two claims here:
1. That "regular laws of nature" are enough to insure that real-world fitness landscapes will be relatively smooth, so that any anti-evolutionary argument based on the assumption of totally random fitness landscapes is unrealistic.
2. That "regular laws of nature" are enough to insure that fitness landscapes will be just the kind needed for darwinian evolution to produce the sort of complexity we see in the biological world.
I would support #1 but not #2. The assumption of a totally random fitness landscape is absurd; this would mean that changing a single nucleotide in an arbitrarily large genome would always have the same sort of effect as changing every nucleotide at once. There would have to be no correlation between genetic similarity and similarity at the phenotype level whatsoever. Empirically we know that this is not true—among other things, sexual reproduction would never work if the genotype-phenotype relation was this brittle. And I think it’s also probably fair to say that, as a rule, changing a single atom in a very large molecule is not going to cause a radical change in the way it interacts with other molecules, and since phenotype seems to be largely determined by interactions between proteins and genes this suggests that this "smoothness" owes a lot to the basic laws of physics and chemistry.
However, the fact that most small changes to the genotype don’t lead to radical changes in phenotype does not rule out the possibility that the fitness landscape would contain plenty of "cliffs" that would spell trouble for Darwinian evolution. It could still be that most or all complex adaptations (the flagellum, the vertebrate eye) are isolated fitness plateaus surrounded by cliffs, which would make macroevolution almost impossible. Since the number of possible complex adaptations is almost certainly tiny compared to the number of possible genotypes, this would still be perfectly compatible with the idea that the fitness landscape is mostly smooth, that on average a given genotype will have about the same fitness as one that is almost identical but differs by a few nucleotides. So, claim #1 Is not enough to guarantee #2.
From all this I conclude that the "strong" no free lunch argument described above, which argues that the NFL theorem is directly relevant to evolution in the real world, does not hold up, since assuming a priori that any random fitness landscape is equally likely to reflect reality is totally implausible. On the other hand, one can make a "weak" argument which just uses the NFL theorem as a sort of metaphor for the fact that darwinian evolution only works well on certain fitness landscapes, and that even the relative smoothness guaranteed by the laws of nature may not be enough to insure that real-world fitness landscapes will be "just right" (although we don’t really know how much flexibility there is here).
[ 16 May 2002, 17:12: Message edited by: Jesse ]
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John Bracht
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posted 16. May 2002 18:50
Jesse,
You missed my point. My argument wasn't that totally random fitness functions apply to the real world, but rather that the fact that they don't is cause for amazement and itself points toward a selection of the "useful" fitness functions from the collection of all possible fitness functions. This is how Kauffman treats the NFL principle. You can't just take the relative smoothness and "evolvability" provided by natural fitness functions for granted--that's the whole point of the NFL principle. You are just begging the question by taking the smoothness of fitness functions for granted (based on real-world experience) and then saying that random fitness functions have no relevance. Of course they don't--but that's the whole point: why, precisely, is this the case? Why can things evolve? Why doesn't our world make use of random fitness functions? The NFL principle is all about stepping outside our realm of experience and considering why things are as they are. There is no obvious reason why smooth fitness functions should exist in our world, and the NFL principle shows that indeed there is no inherent bias in the collection of all possible fitness functions.
Second: you're assuming, along with Wein, that natural laws somehow determine fitness functions. This is false. From the standpoint of the laws of physics, any amino acid sequence is as good as any other. From the standpoint of biological function, this is not the case. As I said earlier, biological function is compatable with the laws of physics, and makes use of the laws of physics (as you point out) but is not reducible to the laws of physics. Physical laws permit any number of alternatives and do not target the functional sequences; that is why polymers can contain information (ruling out real options). Functional logic is encoded into proteins and cannot be reduced to the physical laws of atomic or molecular interactions.
Here's another way to think of it. Consider the computer you're typing from. It consists of many atoms arranged in certain ways and it certainly obeys physical laws. But it is also following a higher-order functional logic that goes beyond mere physical law. This functional logic is a higher-level construct than mere physical law, and it is the shape of this higher-level construct, the functional logic fitness landscape, that must be smooth in order for evolution to occur.
John Bracht
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Jesse
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posted 16. May 2002 19:52
John, in your response you seem to ignore the distinction I was trying to focus on, between claim #1 and claim #2. For example, you say:
quote:
the fact that they don't is cause for amazement and itself points toward a selection of the "useful" fitness functions from the collection of all possible fitness functions. This is how Kauffman treats the NFL principle. You can't just take the relative smoothness and "evolvability" provided by natural fitness functions for granted--that's the whole point of the NFL principle.
Here you talk about "useful" fitness functions and the issue of "evolvability"--but the whole point of my post was that evolvability is a much narrower issue than just the relative amount of smoothness (compared to a totally random, 'spikey' landscape) that #1 says is virtually guaranteed by the regular laws of nature. As I said, it is perfectly possible to imagine that #1 could hold but that the fitness landscape could consist of isolated plateaus which Darwinian processes would not be able to travel between--in that case a slight change to one organism would usually lead to a fairly similar organism, but there would be no way to find a series of small advantageous changes that would lead from, say, a cell that lacked a flagellum to one that had one. Even among the subset of "relatively smooth" landscapes which claim #1 says are guaranteed by regular laws of nature, it might be that only 1 in 10^1000 posess that magic quality of "evolvability." But it would still be true that this relatively smooth subset is tiny compared to the set of all possible fitness landscapes, so a literal use of NFL makes no sense.
If real-world fitness landscapes are of the "useful" type needed for evolvability that might well be "cause for amazement," but the weaker claim of smoothness should not be, in my opinion. Differences between phenotypes are mainly due to the physical properties of different proteins--their shapes, the way they interact with other proteins, etc. A world in which a single-molecule change to a single one of an organism's many proteins would routinely produce a radically different phenotype just doesn't seem compatible with regular laws of nature. How "regular" could these laws be if changing a single atom in a protein (or any other complex molecule) made up of hundreds of individual atoms would lead to changes in shape, interactions, etc. just as unpredictable as changing all of its atoms? And unless your genetic code is fantastically complex, the size of changes in genotype are roughly proportional to the changes in proteins. Something like this would seem to have to be true regardless of what molecules life uses as its basis.
Finally, you said:
quote:
Second: you're assuming, along with Wein, that natural laws somehow determine fitness functions. This is false. From the standpoint of the laws of physics, any amino acid sequence is as good as any other.
Perhaps we're talking past each other here. In a sense, if the reductionist view of nature is correct, the laws of physics + initial conditions determine everything, including the words I choose in this post. Of course there is room for a great deal of historical contingency, both in the choice of initial conditions and also if there is a stochastic element in the laws of physics. And this sort of contingency would show up in fitness landscapes too--adaptations which are useful on earth in our history might not be on a different planet with a different history, even if the laws of physics were the same. Still, claim #1 is that any history with the same laws would involve "relatively smooth" fitness landscapes (by arguments like my one above about the physical properties of biomolecules), although as I said this is not synonymous with landscapes that are "useful" for darwinian evolution.
[ 16 May 2002, 19:55: Message edited by: Jesse ]
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James A. Barham
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posted 16. May 2002 22:00
Jesse:
You made a really interesting comment that I would like to highlight.
You said "organisms cannot be that brittle," or words to that effect, and then went on to add that even changing a single atom in most molecules would not make much difference.
This is an absolutely crucial insight, and conceals the nub of the whole problem. It is precisely the "robustness" of organisms that must be the ultimate explanation for the evolutionary process. Moreover, selection theory tacitly trades on this assumption of robustness and what little plausibility Darwinism has comes wholly from this hidden assumption.
The analogy to the molecule is telling. We must assume, I believe, that the robustness of the organism has precisely the same ultimate source as the robustness of the other structures in nature: namely, dynamical stability. I say this, even while wishing to stress that the specific nature of the robustness of the organism is completely different from that of the rock, and that we have little or no idea how to explain it at present.
Nevertheless, I think it a virtual certainty that it must exist, and I don't see why we shouldn't be able to figure out how to explain it in physical terms some day. To me, this is plain common sense, but to almost everybody else, it seems, it is "vitalism," and thus woolly-headed daydreaming.
[ 16 May 2002, 22:01: Message edited by: James A. Barham ]
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John Bracht
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posted 17. May 2002 12:46
Jesse,
I think you make a useful distinction between the functional landscapes that must be smooth for Darwinian evolution to operate, and the general principle that "small changes lead to small effects," or what you are referring to as the relative smoothness of natural laws. This "small change principle" seems to be a result of (or maybe the cause of) regular natural laws. After all, if small changes in one aspect or quantity caused chaotically large changes in another aspect or quantity, then it would be impossible to speak of general laws at all. Indeed, the very ability of atoms to form stable complexes like proteins and other molecules relies upon the ability of groups of atoms to drop down a smooth energy well as they move closer together, and thus form a stable bond.
In other words, our very experience is so based upon this property of the world, the fact that small changes have small effects, that we take it for granted. It's difficult to even imagine what it would mean for such a principle not to be in effect. However, based on the NFL principle, it seems that we should not take it for granted--for surely such worlds could possibly exist that do not contain this "small change principle". It is not inconcievable that the "laws" of nature could be utterly chaotic (or deterministic but appearing to be totally random in effect). Perhaps this would qualify as a situation in which there are no natural laws. At any rate, there is no obvious reason why this "small change principle" needs be in effect in our universe. So when you say
quote:
How "regular" could these laws be if changing a single atom in a protein (or any other complex molecule) made up of hundreds of individual atoms would lead to changes in shape, interactions, etc. just as unpredictable as changing all of its atoms? And unless your genetic code is fantastically complex, the size of changes in genotype are roughly proportional to the changes in proteins. Something like this would seem to have to be true regardless of what molecules life uses as its basis.
I point to the fact that you are assuming some sort of "small change principle" when you invoke the fact that proteins or molecules even exist. You're still considering only a certain subset of fitness functions--but there is no a priori reason (as far as I can tell) to make that assumption. The "small change principle" represents only a small fraction of possible ways the world can be (thus, corresponding to only a small subset of fitness functions in the NFL principle).
In other words, not even the "small change principle" can be taken for granted. It is a necessary, but not sufficient, requirement for evolvability. I agree with you that once we have this "small change principle" we might still have very rugged fitness landscapes--as we observe in the real world when a minor, even conservative amino acid substitution in the active site of an enzyme causes it to stop working from a functional standpoint yet doesn't alter the overall structure or other molecular properties. While Kauffman does seem to focus on these higher level fitness functions (and expresses amazement at the fact that they are smooth enough for evolution to work), I suggest that even this lower-level, "small change principle" requirement cannot be taken for granted. Certainly, it is a necessary precondition for anything like molecules and life to exist--but that is not enough to explain why it exists. We need to be careful not to beg the question.
John Bracht
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Jesse
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posted 20. May 2002 15:15
John Bracht:
quote:
In other words, our very experience is so based upon this property of the world, the fact that small changes have small effects, that we take it for granted. It's difficult to even imagine what it would mean for such a principle not to be in effect. However, based on the NFL principle, it seems that we should not take it for granted--for surely such worlds could possibly exist that do not contain this "small change principle". It is not inconcievable that the "laws" of nature could be utterly chaotic (or deterministic but appearing to be totally random in effect). Perhaps this would qualify as a situation in which there are no natural laws. At any rate, there is no obvious reason why this "small change principle" needs be in effect in our universe.
Sure, we shouldn't take it for granted that we live in a universe which follows regular, elegant laws instead of one in which events occur in a totally choatic and unpredictable fashion. However, this issue is more akin to that of cosmological fine-tuning; it has little or nothing to do with evolution. In fact, it is probably more of a metaphysical question than a scientific one. Certainly it's not the job of evolutionary biologists to explain this feature of our universe; as with scientists in all other fields, they take the laws of nature for granted.
In any case, I strongly disagree that the NFL theorem sheds any new light on this issue--if anything, it only serves to confuse things. For example, how would you justify using a uniform probability distribution on the set of all fitness landscapes? I noticed that in Dembski's response to Wein he didn't offer a clear answer to the question of whether he has a "uniform probability method" of quantifying specified information separate from the method which uses the actual probabilities induced by the laws of nature--perhaps you have some insight into this? But even if you think a uniform probability distribution on the set of all possible "universes" somehow makes sense, how does this translate into a uniform probability distribution on fitness landscapes? In a chaotic lawless universe I don't see how the concept of "the probability that a particular genome will survive and reproduce in a particular environment" (ie 'fitness') could possibly make sense--how could there be stable entities capable of self-replication in such a universe? What would their "environment" be? I just don't see what set of assumptions you'd have to make if you wanted to defend a literal (as opposed to metaphoric) use of the NFL theorem as somehow being relevant to evolution; if you do want to defend this idea, you're going to have to spell out your assumptions more clearly.
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Janitor@MIT
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posted 23. May 2002 13:02
I apologize because my question appears to be somewhat tangential but I didn’t want to start a topic just to clear up my confusion (and with nothing else positive to contribute).
Its basically a methodological question: Since its pretty standard procedure in many sciences and engineering to begin with a rather featureless parameter space (simply on the assumption that fewer assumptions are better assumptions), which is then modified into a product space via projection of the induced values of the relevant variables (if not initially all observed variables), then why is it “illegitimate” for Dembski to follow the same procedure? Does the same objection apply to, say, quantum statistics or information theory, e.g.?
My sister (a research oncologist) informs me (what I already knew) that they never have a uniform probability distribution to begin with--so they invent one! They use it to represent a null hypothesis against which they can compare their data/inferences. I understand that this is a routine procedure in clinical research (and I know it is in engineering).
But there is something strange going on here, isn’t there? If Darwin insisted, e.g., that mutations occur at random wrt fitness, then isn’t he really imposing uniformity on the underlying “hypothesis space”? But isn’t that the same as saying that his theory is the null hypothesis?! I’m getting lost here…
It seems to me that Dembski could only assume one other thing if he doesn’t begin with a uniform space: specifically he seems to be required (by his critics) that he assume the validity of the theory (or in any case the most favorable assumptions) he is purportedly testing!
But… but… that theory seems to be indistinguishable from the null hypothesis (?!). (Unless, as some have suggested, the evolution of life is somehow “foreordained.” Even Darwin entertained the idea, even though he also explicitly militates against it in Origin.)
I hate statistics! Am I confused or what?! No doubt I am. (Or is it possible that the confusion really lies somewhere else?) I hate to be such a nuisance (actually I don't mind it at all), but any help in this area would be greatly appreciated.
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Erik
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posted 23. May 2002 18:07
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Janitor@MIT: Its basically a methodological question: Since its pretty standard procedure in many sciences and engineering to begin with a rather featureless parameter space (simply on the assumption that fewer assumptions are better assumptions), which is then modified into a product space via projection of the induced values of the relevant variables (if not initially all observed variables), then why is it “illegitimate” for Dembski to follow the same procedure? Does the same objection apply to, say, quantum statistics or information theory, e.g.?
Your mathematical description makes little sense. (E.g., "...modified into a product space via projection of the induced values of the relevant variables..."; product spaces are not formed by projection. I believe you would communicate much more efficiently if you did not try to dress up your ideas in seemingly eloborate mathematical jargon.) Aside from that, there would be nothing illegitimate with Dembski following the only possible approach to do science, namely to formulate a descriptive model. But that is not what Dembski is trying to do. In fact, one of the strongest common denominators of the ID movement is the lack of interest in descriptive models (instead the interest is directed to ontological issues such as the nature of intelligence and the nature of nature).
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Janitor@MIT: My sister (a research oncologist) informs me (what I already knew) that they never have a uniform probability distribution to begin with--so they invent one! They use it to represent a null hypothesis against which they can compare their data/inferences. I understand that this is a routine procedure in clinical research (and I know it is in engineering).
I fail to see the relevance.
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Janitor@MIT: But there is something strange going on here, isn’t there? If Darwin insisted, e.g., that mutations occur at random wrt fitness, then isn’t he really imposing uniformity on the underlying “hypothesis space”? But isn’t that the same as saying that his theory is the null hypothesis?! I’m getting lost here…
No. When biologists say that mutations are random with respect to fitness, they do not actually mean that all mutations are equally probable. Nor do they mean that all fitness effects of a mutation are equally probable. What they actually mean is that it is not required by their theory that mutations are biased to those that confer higher fitness--the theory works anyway. And since the theory works anyway, it is unnecessary to assume such a bias. (Here the biologists could probably communicate more efficiently if they actually said what they mean!)
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Janitor@MIT: It seems to me that Dembski could only assume one other thing if he doesn’t begin with a uniform space: specifically he seems to be required (by his critics) that he assume the validity of the theory (or in any case the most favorable assumptions) he is purportedly testing!
Well, that is the standard way to test a theory. To test the theories T1 and T2, we first assume--for the sake of the argument--that T1 is true and try to determine what the world should look like then. Then the same thing is done for T2. Which fits the actual appearance of the world best?
Erik
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Jesse
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posted 23. May 2002 23:24
Janitor, I'm not really sure what you mean--where in science is it standard procedure to assume a uniform probability distribution in absence of any knowledge of the actual probabilities of one type of outcome vs. another? You mention "null hypotheses" but these have nothing to do with assuming uniform probabilities--as far as I know they're usually about assuming there is no causal connection between different events, and then seeing how well that assumption matches reality. For instance, if we know the recovery rate from a particular disease is generally 73%, and we wanted to know if that rate could be improved through the use of a certain drug, the "null hypothesis" would be that even among a group of people who take the drug the recovery rate will still be 73%. On the other hand, the "uniform probability method" suggest that even before knowing the overall recovery rate, we should assume the "natural" recovery probability would be exactly 50%, and that any significant deviations from this rate indicate an intelligence has been tampering with the numbers. This resembles nothing I have ever seen in mainstream science.
Of course, Dembski has not specifically said he has a "uniform probability method"--that's just Richard Wein's interpretation of his puzzling arguments about CSI being "smuggled into the fitness landscape" in NFL. His response to Wein failed to clarify this issue (see section 5 on p. 16 of the pdf)--does anyone understand what he meant when he talks about a "natural" probability measure on the phase space? How would this be determined exactly? What is the "natural" probability measure on the set of all possible real-world fitness landscapes, or the set of all possible laws of physics?
[ 23 May 2002, 23:38: Message edited by: Jesse ]
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