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Author
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Topic: Genetic Algorithms and fitness functions with coupled variables
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William A. Dembski
Member
Member # 7
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posted 04. March 2002 23:30
Jesse:Regarding the existence of CSI in the universe, the job of the Darwinist is to show that the C in CSI is really not all that complex. The job of the design theorist is to show that with respect to the laws of nature (characterized by chance and necessity), the C cannot be decreased below the universal complexity bound (500 bits). So does CSI exist in nature? Certainly, it might exist relative to the natural laws operating in nature. Now, as a practical matter, we may be ignorant of all the laws operating in nature. So, we might be wrong in ascribing CSI to something. But the mere possibility that we've missed some law is, in my view, no reason to dismiss the complexity-specification criterion. Scientists committed to naturalism, on the other hand, will be differently inclined. Fine. I'm not trying win the world, only a portion of it. In chapter 5 of NFL I develop some techniques for calculating the probabilities connected with discrete combinatorial objects. I focus on the uniform distribution, but that's not essential to the argument. As always with specified complexity, the issue is to establish complexity/improbability with respect to all relevant probability distributions. I argue for the specified complexity of the bacterial flagellum. Critics may contend that I've not sufficiently exhausted the relevant probability distributions. That brings up the question of again of burden of proof in probability arguments. Darwinists seem to think that because their mechanism has been "overwhelmingly confirmed," that once cumulative selection is brought in, Mount Improbable can always be climbed gradually. But the presumption that probabilities can always be dissolved in this way it seems can be turned around. Why not instead presume that the probabilities are small until a gradual Darwinian pathway up Mount Improbable is actually demonstrated (and not merely gestured at with a just-so story)? As for the universe being fine-tuned for Darwinism to succeed, I agree that this is not where the action is (in fact I indicated as much in my last post where I stressed that it's an empirical matter whether the fitness functions are smooth). Jesse writes: "It seems rather odd to me to say that the burden is on 'Darwinists' to explain the origin of the laws of physics!" That's not where the burden lies. The burden lies on the the Darwinists and other naturalists to explain why the laws of physics have the form they do so that, if Darwinism does indeed provide the mechanism for the emergence of biological complexity, that mechanism induces life to flourish. Jesse raises the example of showflakes in this context. The fact is that a universe whose laws facilitate Darwinism or one that permits snowflakes is going to be very special. Indeed, it seems that if the laws of physics are tinkered with only a little, one ends up with a universe of sludge in which nothing interesting ever happens. But how does one assign probabilities to the laws of physics. Usually this lands one in the waters of metaphysics, and for this reason I tend to avoid arguments that try to impose probabilities on the laws of physics. Still, a more qualititative regress argument of the sort I made in the last post seems to me compelling. As for the principle of indifference , I don't put much stock in it here or elsewhere (historically, there've always been problems with trying to apply it). Even so, to a first approximation it is often the best we can do not to bias our conclusions. Thus, if one is going to argue about probability distributions that privilege smooth fitness functions, then it seems that the principle of indifference is being violated and I suppose one could even argue that Occam's razor is being violated (indifference and uniform probability being simpler than concentrating probability in any one place). This is all disputable, but it helps keep philosophers of probability in business. The heart of the matter remains some form of irreducible complexity where small changes from a physical vantage can lead to sharp discontinuities from a functional vantage. Jesse writes: "The regular laws of nature insure that changing a single atom in a complex molecule will not tend to radically alter the way this molecule interacts with other molecules." This seems false, if not at the atomic level then at the molecular level where the nuts and bolts action of life takes place. A single amino acid change is enough to induce sickle cell anemia. A single omitted word can radically alter a text (publishers of the King James Bible in the 17th century were harshly fined for omitting the word "not" from the commandment against adultery). Prediction: Within the next two years work on certain enzymes will demonstrate overwhelmingly that they are extremely isolated functionally, making it highly implausible for Darwinian and other gradualistic pathways to evolve into or out of them. This will provide convincing evidence for specified complexity.
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Erik
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Member # 160
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posted 05. March 2002 10:23
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William A. Dembski (first reply to me): With respect to the natural probability measure (usually a uniform probability) on the space, the target represents an instance of specified complexity. With respect to the new probability induced by the fitness function, however, it does not. The point of natural mechanisms is not to generate specified complexity but to dissolve the very notion (cf. Dawkins's metaphor of climbing Mount Improbable -- Mount Improbable really isn't all that improbable to climb once one figures out a gradual Darwinian route). My point in invoking NFL is that the search for the target in the original search space gets displaced by a GA to searching the space of fitness functions over that space, thus intensifying the search problem rather than resolving it.
Dr. Dembski, it makes little sense to say that the space of fitness functions must be searched. When we try to solve a problem with a GA, the fitness function represents the problem. We cannot choose the fitness function arbitrarily, because then we would also be choosing an arbitrary problem. Once we have decided which problem to try to solve, the fitness function is fixed. I believe that you have unwittingly mislead yourself by naming a location in the search space "the target" and by thinking of a fitness function as "guide" to the target, rather than as a representation of a problem.
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William A. Dembski: There's no place in my writings where one "calculates the specified complexity." Complexity as a logarithmic recalibration of probability does get calculated.
Are you saying that "specified complexity" is not a quantity represented by a real number, but a predicate that can only be "true"/"false" or "present"/"absent"?
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William A. Dembski: As for doing the actual calculation for determining the probability of hitting the target relative to the GA, that will depend on the particulars of the fitness function and the way the search algorithm makes use of the fitness function (in practice Monte Carlo simulations will be the way to go). Frankly, though, the burden is not on the design theorist to do that calculation. Nor is it of interest to the Darwinian if that probability of hitting the target is very small. The point of the GA is to hit the target with reasonable probability (in which case the specified complexity of the target dissolves).
I am not asking for the actual calculation. I am asking for exactly which probability the actual calculation would need to determine. Did I get it exactly right with my equation (2)? Is equation (2) precisely the equation you would use to determine if a location visited by the GA had specified complexity? If not, please provide the correct equation. It may or may not be the design theorist's burden to do the actual numerical calculation, but the burden of defining the probability that is to be computed is solely yours, Dr. Dembski.
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William A. Dembski: My argument in NFL is that if that probability is reasonably high (as it should be for a useful GA), then the search on the original phase space was transferred to the space of fitness functions. There's no magic to evolutionary computation. This is being admitted even by fans of evolutionary computation like Geoffrey Miller:
"Genetic algorithms are rather robust search methods for [simple problems] and small design spaces. 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 as no general-purpose genetic algorithm."
Dr. Dembski, GA designers have no trouble at all knowing which fitness function to use--it is pretty much determined once they have decided which problem they will be attempting to solve. What can be difficult is knowing how to represent the space of conceivable solutions to the problem in question and possibly also to choose the selection scheme (roulette selection? tournament selection? ...). But this problem has no analogue in biological evolution, since the relevant genetics is taken as a given (and the DNA representation of organisms is very flexible, allowing for anything from archaebacteria to giraffes to be represented). Instead the problem has its analogue in abiogenesis research, where it will either be solved by showing how the genetic code is a result of physico-chemical phenomena or not solved.
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William A. Dembski (in reply to Jesse): That brings up the question of again of burden of proof in probability arguments. Darwinists seem to think that because their mechanism has been "overwhelmingly confirmed," that once cumulative selection is brought in, Mount Improbable can always be climbed gradually. But the presumption that probabilities can always be dissolved in this way it seems can be turned around. Why not instead presume that the probabilities are small until a gradual Darwinian pathway up Mount Improbable is actually demonstrated (and not merely gestured at with a just-so story)?
Is your proposition to turn this around limited to mainstream evolutionary biology or should we also take as the default position that lightning is extremely improbable with respect to all known physical models until someone can actually demonstrate that is not so (and not merely gestured at with a very idealized model)? What about the existence of an Intelligent Designer of life on Earth? Perhaps that should also be taken to be extremely improbable until someone can actually show that it is not.
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William A. Dembski (in reply to Jesse): Prediction: Within the next two years work on certain enzymes will demonstrate overwhelmingly that they are extremely isolated functionally, making it highly implausible for Darwinian and other gradualistic pathways to evolve into or out of them. This will provide convincing evidence for specified complexity.
Do you have any particular enzymes in mind?
Erik
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William A. Dembski
Member
Member # 7
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posted 05. March 2002 15:03
Erik writes: "It makes little sense to say that the space of fitness functions must be searched. When we try to solve a problem with a GA, the fitness function represents the problem."
Not so. When Edward Altshuler writes a GA to to find an antenna that radiates uniformly over a hemisphere, he is simply interested in finding such an antenna. A fitness function that would "represent" this problem could be merely an indicator function which evaluates to 1 when the antenna radiates uniformly and 0 otherwise. Edward Altshuler solved this problem by defining a fitness function that measures degree to which an antenna radiates uniformly. That fitness function did not simply fall out of the sky, but was carefully constructed on the basis of Altshuler's scientific knowledge. The fitness function he finally chose did not represent the problem – in finding it Altshuler actually solved the problem. Once he had the right fitness function, the problem was solved. (Do a Google search on "crooked wire genetic antennas")
As for, Is specified complexity a number or a predicate? it is a predicate whose truth value is determined among other things by calculating a probability or set of probabilities relative to the probability distributions that might relevant to characterizing an event's chance occurrence (the probabilities also being construable as complexities). I'm therefore not sure what you're asking when you want me to look over your calculation. Presumably you know how to calculate probabilities. The issue is whether it's reasonable to think that you've exhausted the relevant probabilities and whether the event in question is also specified. Darwinists usually try to sink specified complexity on the question of probabilities.
Erik continues: "GA designers have no trouble at all knowing which fitness function to use--it is pretty much determined once they have decided which problem they will be attempting to solve." Did you read my previous quote by Geoffrey Miller? Miller writes: "Genetic algorithms are rather robust search methods for [simple problems] and small design spaces. 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 as no general-purpose genetic algorithm."
In the same essay Miller continues: "The fitness function must embody not only the engineer's conscious goals, but also her common sense. This common sense is largely intuitive and unconscious, so is hard to formalize into an explicit fitness function. Since genetic algorithm solutions are only as good as the fitness functions used to evolve them, careful development of appropriate fitness functions embodying all relevant design constraints, trade-offs and criteria is a key step in evolutionary engineering." So according to Miller the design is in the choice of fitness function, just as in the Altshuler case I related above. You can find the references in my essay "Why Natural Selection Can't Design Anything" in the ISCID archive.
As for whether I have any particular enzyme in mind that will help overturn Darwinism, yes I do. I also know the researcher who is working on that enzyme. Once the results are published, I'll be sure to announce it on this board.
I'm off to Canada for a speaking tour and won't be online with this board till then. I feel I've gone around on these topics with Erik and Jesse enough, so I don't expect to post on this thread again. I trust we'll be encountering each other on other threads.
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Frances
Member
Member # 169
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posted 06. March 2002 01:19
quote:
Originally posted by William A. Dembski:
Jesse:
Now, as a practical matter, we may be ignorant of all the laws operating in nature. So, we might be wrong in ascribing CSI to something. But the mere possibility that we've missed some law is, in my view, no reason to dismiss the complexity-specification criterion. Scientists committed to naturalism, on the other hand, will be differently inclined. Fine. I'm not trying win the world, only a portion of it.
Am I correct to state that your argument in NFL and the design inference was that the filter would not suffer from false positives?
I believe that our lack of knowledge can be a reason why the filter would lead to false positives. Only when we learn about the natural mechanisms do we realize that what appeared designed was in fact quite natural.
In fact the 'we don't know' seems to be a category missing from the design inference filter as far as I can tell.
Wilkins and Elsberry have published a paper "The advantages of theft over toil: the design inference and arguing from ignorance " [Forthcoming - Biology and Philosophy 2001 which provides for a logical alternative to the filter.
If ID is infered through the elimination of chance and regularity how does one deal with yet unknown regularity? That is how does one deal with our ignorance of these matters?
To me the reliability of the ID filter seems far from obvious, certainly a claim that the filter does not lead to false positives seems overly optimistic.
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That brings up the question of again of burden of proof in probability arguments. Darwinists seem to think that because their mechanism has been "overwhelmingly confirmed," that once cumulative selection is brought in, Mount Improbable can always be climbed gradually. But the presumption that probabilities can always be dissolved in this way it seems can be turned around. Why not instead presume that the probabilities are small until a gradual Darwinian pathway up Mount Improbable is actually demonstrated (and not merely gestured at with a just-so story)?
How would this help ID. If ID is infered from the elimination of chance and regularity then one has to deal with the possible scenarios. If ID wants to argue that a scenario is unlikely and thus infer design, would it not be up to the ID'er to provide for supporting evidence?
I believe that one of the main weaknesses in the ID filter lies in the elimination of alternatives. Unless one can provide for the probabilities for these scenarios how can one eliminate them?
[ 06 March 2002, 01:25: Message edited by: Frances ]
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Dene Bebbington
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Member # 168
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posted 06. March 2002 09:46
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Originally posted by William A. Dembski:
Erik writes: "It makes little sense to say that the space of fitness functions must be searched. When we try to solve a problem with a GA, the fitness function represents the problem."
Not so. When Edward Altshuler writes a GA to to find an antenna that radiates uniformly over a hemisphere, he is simply interested in finding such an antenna. A fitness function that would "represent" this problem could be merely an indicator function which evaluates to 1 when the antenna radiates uniformly and 0 otherwise. Edward Altshuler solved this problem by defining a fitness function that measures degree to which an antenna radiates uniformly. That fitness function did not simply fall out of the sky, but was carefully constructed on the basis of Altshuler's scientific knowledge. The fitness function he finally chose did not represent the problem – in finding it Altshuler actually solved the problem. Once he had the right fitness function, the problem was solved. (Do a Google search on "crooked wire genetic antennas")
[…]
I couldn't find the whole text of this paper, only an abstract. From what you say above it seems that the fitness function is a way of determining how well a proposed solution meets the requirements given by the problem. Are you saying that Altshuler actually designed and/or created an antenna that radiates uniformly in order to come up with a fitness function to be used with the GA? If not, then what do you mean by saying that " Once he had the right fitness function, the problem was solved."?
--
Dene
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Jeremy Alder
Member
Member # 32
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posted 06. March 2002 17:06
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Originally posted by Frances:
Am I correct to state that your argument in NFL and the design inference was that the filter would not suffer from false positives?
I believe that our lack of knowledge can be a reason why the filter would lead to false positives. Only when we learn about the natural mechanisms do we realize that what appeared designed was in fact quite natural.
In fact the 'we don't know' seems to be a category missing from the design inference filter as far as I can tell.
Wilkins and Elsberry have published a paper "The advantages of theft over toil: the design inference and arguing from ignorance " [Forthcoming - Biology and Philosophy 2001 which provides for a logical alternative to the filter.
If ID is infered through the elimination of chance and regularity how does one deal with yet unknown regularity? That is how does one deal with our ignorance of these matters?
To me the reliability of the ID filter seems far from obvious, certainly a claim that the filter does not lead to false positives seems overly optimistic.
Frances,
Bill Dembski adresses the unpublished Elseberry paper you reference, as well as the other concerns you bring up, in No Free Lunch. I think reading what Dr. Dembski has already published would be helpful to you.
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Frances
Member
Member # 169
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posted 07. March 2002 00:40
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Originally posted by Jeremy S. Alder:
Frances,
Bill Dembski adresses the unpublished Elseberry paper you reference, as well as the other concerns you bring up, in No Free Lunch. I think reading what Dr. Dembski has already published would be helpful to you.
The paper has been accepted for publication and as I understand has been published. I wish that people though would have the courtesy to provide for an argument rather than refer to a claim like "this has already been addressed".
Let me ask you, did Dembski drop the "no false positives". I have seen Dembski argue as well that our lack of knowledge would lead to false positives but that such is inevitable.
So while under perfect knowledge the ID inference would indeed provide us with no false positives, under more mundane circumstances it seems that the ID filter is hardly that reliable per se.
So unless we believe that our knowledge is sufficient we should not jump to conclusions of ID.
[ 07 March 2002, 09:13: Message edited by: Moderator ]
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Moderator
Administrator
Member # 1
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posted 07. March 2002 09:11
OK. This thread is starting to get off topic. Frances, you may have questions that you would like to see Dr. Dembski address, but they are too tangential for the original topic of this thread.
This is a warning to you as I have seen a pattern in several of your posts. You are free to ask questions of clarification in Brainstorms if the questions pertain to the topic at hand.
If I continue to see this pattern of negative tangential posting, I will assume that you are here for reasons that are not compatible with the spirit of Brainstorms and I will take the appropriate action.
[ 07 March 2002, 09:19: Message edited by: Moderator ]
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Jeremy Alder
Member
Member # 32
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posted 07. March 2002 17:23
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Originally posted by Frances:
The paper has been accepted for publication and as I understand has been published. I wish that people though would have the courtesy to provide for an argument rather than refer to a claim like "this has already been addressed".
Let me ask you, did Dembski drop the "no false positives". I have seen Dembski argue as well that our lack of knowledge would lead to false positives but that such is inevitable.
Frances,
You asked some good questions about Dembski's ideas and I was just pointing to a place where you can find answers to those questions - Dembski's book. I wish I had time to summarize what is in the book for you, but I don't. Perhaps when I am done with my own homework I can do yours for you as well. Until then...
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Frances
Member
Member # 169
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posted 07. March 2002 22:44
quote:
Originally posted by Jeremy S. Alder:
quote:
Originally posted by Frances:
The paper has been accepted for publication and as I understand has been published. I wish that people though would have the courtesy to provide for an argument rather than refer to a claim like "this has already been addressed".
Let me ask you, did Dembski drop the "no false positives". I have seen Dembski argue as well that our lack of knowledge would lead to false positives but that such is inevitable.
Frances,
You asked some good questions about Dembski's ideas and I was just pointing to a place where you can find answers to those questions - Dembski's book. I wish I had time to summarize what is in the book for you, but I don't. Perhaps when I am done with my own homework I can do yours for you as well. Until then...
Looking forward to your contributions. Only through looking at the arguments and counter arguments can we find a better argument.
I appreciate your willingness to help me in this area. In fact I have found this forum to be an excellent place to discuss and learn about ID.
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Erik
Member
Member # 160
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posted 08. March 2002 04:05
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Erik: It makes little sense to say that the space of fitness functions must be searched. When we try to solve a problem with a GA, the fitness function represents the problem.
William A. Dembski: Not so. When Edward Altshuler writes a GA to to find an antenna that radiates uniformly over a hemisphere, he is simply interested in finding such an antenna. A fitness function that would "represent" this problem could be merely an indicator function which evaluates to 1 when the antenna radiates uniformly and 0 otherwise. Edward Altshuler solved this problem by defining a fitness function that measures degree to which an antenna radiates uniformly. That fitness function did not simply fall out of the sky, but was carefully constructed on the basis of Altshuler's scientific knowledge. The fitness function he finally chose did not represent the problem – in finding it Altshuler actually solved the problem. Once he had the right fitness function, the problem was solved. (Do a Google search on "crooked wire genetic antennas")
You are wrong, Dr. Dembski. GAs are used for optimization problems. Altshuler started with a technological problem that he wanted to solve (namely, "how do I construct an antenna that radiates uniformly over a hemisphere?"). In order to solve his technological problem he figured out a way to represent the space conceivable antennas and then he translated the technological problem into a mathematical problem. This is where the fitness function comes in, because it measures how good a technological solution Altshuler considered particular mathematical representations of technological solutions to be. Thus, the mathematical problem is to find the optimum, or at least a high value, of the fitness function. Therefore the fitness function represents the problem to be solved. Had Altshuler chosen a different fitness function, he would have solved a different problem. How can you disagree with this, Dr. Dembski?
Look up any book on Linear Programming and you will probably find lots of examples of how simple real world optimization problems are translated into (linear) mathematical optimization problems. Is the problem solved once the objective function (this is the general name--for GAs it is often called "fitness function") is specified? No, lest there would be no need to actually learn LP algorithms such as the simplex method. Once the objective function is specified we have defined the problem to be solved. Then the problem is solved by some method. The situation with GAs is completely analogous. Once we have specified the fitness function the problem to be solved is fixed. Then the GA is applied in an attempt to actually solve it.
Now, it is true that the translation of a technological optimization problem into a mathematical optimization problem can require detailed knowledge (in fact, often the solution to the mathematical problem leads to a revision of the mathematical formulation rather than to a solution to the technological problem), but that has absolutely nothing to with the abilities (or lack thereof) of GAs to solve problems. GAs do well or bad in optimizing fitness functions regardless of whether the fitness functions are good representations of the technological problem or not.
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William A. Dembski: As for, Is specified complexity a number or a predicate? it is a predicate whose truth value is determined among other things by calculating a probability or set of probabilities relative to the probability distributions that might relevant to characterizing an event's chance occurrence (the probabilities also being construable as complexities). I'm therefore not sure what you're asking when you want me to look over your calculation. Presumably you know how to calculate probabilities. The issue is whether it's reasonable to think that you've exhausted the relevant probabilities and whether the event in question is also specified. Darwinists usually try to sink specified complexity on the question of probabilities.
Thanks for the clarification regarding predicates. I give up on trying to formulate my question on probability distributions.
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Erik: GA designers have no trouble at all knowing which fitness function to use--it is pretty much determined once they have decided which problem they will be attempting to solve.
William A. Dembski: Did you read my previous quote by Geoffrey Miller? Miller writes: "Genetic algorithms are rather robust search methods for [simple problems] and small design spaces. 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 as no general-purpose genetic algorithm."
It was wrong of me to state that "GA designers have no trouble at all knowing which fitness function to use". It could well be difficult to translate the technological problem into a mathematical problem, but the point is that the fitness function is merely a way to represent the "goodness" of conceivable solution mathematically and that it is pretty much determined (which does not necessarily implies that there's on problem in finding it, though) once the problem to be solved has been stated.
I've read your quote, in fact, I've read the whole article by the evolutionary psychologist Geoffrey Miller. Your quote is irrelevant--it has nothing to do with the difficulty (or lack thereof) in choosing the appropriate fitness function. It has to do with designing genetic algorithms, not choosing the fitness function. It may or may not be easy to implement a particular genetic algorithm, but that has nothing to do with how hard/easy it is to choose the appropriate fitness function. (Completely analogously, it may or may not be easy to implement the simplex algorithm for linear programming, but that has nothing to do with how hard/easy it is to choose the appropriate objective function to optimize over.)
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William A. Dembski: In the same essay Miller continues: "The fitness function must embody not only the engineer's conscious goals, but also her common sense. This common sense is largely intuitive and unconscious, so is hard to formalize into an explicit fitness function. Since genetic algorithm solutions are only as good as the fitness functions used to evolve them, careful development of appropriate fitness functions embodying all relevant design constraints, trade-offs and criteria is a key step in evolutionary engineering." So according to Miller the design is in the choice of fitness function, just as in the Altshuler case I related above. You can find the references in my essay "Why Natural Selection Can't Design Anything" in the ISCID archive.
I have only read the internet version of Miller's paper, but I believe that you should not have begun the quote with a capital 'T' as it is not the beginning of a sentence.
Miller nicely illustrates my point and contradicts your claims. You claimed that the fitness function is not a representation of the problem to be solved. Yet, the quote you provide is precisely about the fact that the fitness function represents the problem to be solved. Indeed, in the paragraph immediately preceeding the one you quoted Miller commented: "If the fitness function does not realistically reflect the real-world constraints and demands that the phenotypic designs will face, the genetic algorithm may deliver a good solution to the wrong problem." How can the wrong fitness function yield a good solution to the wrong problem if the fitness function does not represent the problem to be solved, Dr. Dembski? It cannot.
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William A. Dembski: I'm off to Canada for a speaking tour and won't be online with this board till then. I feel I've gone around on these topics with Erik and Jesse enough, so I don't expect to post on this thread again. I trust we'll be encountering each other on other threads.
For what it's worth, I do not share the feeling that we've gone around on these topics. In fact, I think we are making progress. Thus, if you change your mind I will be interested in continuing this discussion.
Erik
[ 08 March 2002, 04:12: Message edited by: Erik ]
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