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Author
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Topic: Simulating Self Assembly
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Moderator
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posted 19. February 2003 07:17
My sense is that this thread has been running out of steam for some time. It will be closed tomorrow.
Warren, I am a little worried about the pattern that I see with the threads that you have started. This is how I see the pattern developing at the end of each of your threads:
1. You insist that your critics are wrong because they just don't understand the mathematics behind the argument
2. Your critics point out that there are no concrete mathematics for them to understand: you've not provided it for everyone else to analyze
I'm going to ask you in the future to avoid the repeated refrain "you don't understand the mathematics" until you've provided a mathematical system for the public to observe. The reason the alchemists weren't convincing is that they kept their methods/experiments private, making extravagent claims without making the scientific process a public one. There results could not be confirmed or criticized.
Please don't resort to this method when dealing with your critics on Brainstorms.
[ 19. February 2003, 07:19: Message edited by: Moderator ]
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warren_bergerson
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posted 19. February 2003 09:59
Moderator,
The basic mathematics underlying design science has been presented here. In summary this mathematics consists of
1. Any assembly or operating process in any biological system can be reduced to or expressed as or reduced to a set C or automated assembly instructions. [Any operation of any biological system can be modeled by sets of assembly/operational instructions which are ‘dynamic and teleological’ causal relationships. ]
2. Any change in a set of assembly process from C1 to C2 can be modeled as simulated by a real time multiple-variation selection TA system. [Any change in any dynamic and teleological causal relationship can be modeled and simulated by a complex mathematical algorithm TA.]
3. Any operation of any TA system can be modeled by a set of automated assembly instructions. [It is possible to reduce any biological change process to known physical chemical laws or processes.]
Components 1 and 3 are basic if somewhat complex computer modeling/simulation techniques. The TA system, while it may be a bit unconventional, is a relatively simple variation of the basic variation-selection concept used in GA’s. I have presented, at least in outline form, all the concepts underlying the above three components. This is basic, fundamental, rigorous mathematics. It has absolutely no similarity to the techniques used to support alchemy and your comment to that effect is inappropriate and out of line.
My comments on ‘understanding the mathematics presented’ were intended to point out that mathematics and mathematical concepts 1)are often more complex and more difficult to understand than is sometimes recognized, and 2)understanding one type of mathematics does not automatically imply understanding another form of mathematics. There are a number of individuals who regularly post here who not infrequently attempt to dismiss any idea with which they disagree based on their credentials rather than based on addressing the issue involved. Mathematics, I was trying to point out, is too complex and too diverse for unsupported subjective opinions to carry much weight.
The TA system mathematics I have presented here is based on ‘simple’ mathematical concepts and principles which should, IMO, be comprehensible by anyone with a basic understanding of set theory, mathematical modeling, and computer simulation. Where you go with this basic type of mathematics once you move beyond basic concepts, is something even most mathematicians will have difficulty visualizing unless they actually begin to work with it.
As I have been attempting to explain here for almost a year, one of the fundamental issues in design is the ‘volume of information processing’. Darwinian approaches suggest the development and operation of biological systems can be explained by low volume between generation processes. Traditional ID supporters have argued that biological systems are more complex than can be explained by Darwin and have suggested the additional information processing is provided by ‘external designers’. I am proposing that the additional information processing arises from the logical equivalent of within lifetime variation selection processing.
In this thread I have introduced the basic mathematics needed 1)to measure the complexity of a biological systems (the complexity of automated assembly instructions), 2)a method of modeling the changes in assembly instructions (the TA system), and 3) a method of testing and validating the materialistic reality of TA systems. It is not, IMO, surprising that individuals will have difficulty understanding this ‘new math’ even if it is based on standard, rigorous mathematical concepts. Other than the normally complexity of a new form of math, TA mathematics suggests that many of ‘preconceptions’ about biological systems are wrong.
As a simple example, TA mathematics suggests that individual cells information processing capabilities that are far exceed the processing capabilities of the biggest computers built by man. These processing capabilities combined with a relatively small amount of initial information, allow these systems to ‘design’ complex multi-cellular organisms not in millions of years, but in the lifetime of the organism.
I have provided basic techniques for 1)demonstrating that biological cells are extremely complex, 2)for modeling and explaining the complex processes responsible for changing this complexity, and finally, 3)for demonstrating that the complex processes are explainable in terms of known physical -chemical processes. It is not, IMO, surprising that the techniques being discussed are not immediately understood by every academic with a credential. The lack of understanding of the techniques presented is not surprising even for individuals who understand basic principles on which the techniques are based.
SUMMARY
You are, of course, the moderator and you decide what can and what can not be discussed here. Even when I have not agreed with your views I have tried to respect them. You can ban the discussion here of TA mathematics.
I would suggest that as an alternative to banning the discussion of TA mathematics we change the focus of the discussion from ‘high level applications’ to a discussion of basic concepts and principles. The purpose of the discussion would be to compare and contrast the basic concepts and principles underlying TA mathematics to the basic concepts and principles underlying more conventional forms of mathematical analysis.
Analysis based on TA mathematics suggests biological systems are extremely complex because they contain extremely powerful, but materialistic, information processing or ‘intelligent design’ processes. This would appear to contradict conventional evolutionary and genetic concepts as well as conventional ID concepts.
I claim that analysis based on TA mathematics is sound and rigorous and the conclusions reached are logical and supported by available evidence. There are, it appears, a number of individuals who disagree with my claims. It seems reasonable to conclude that either 1)some of the basic concepts and principles underlying my analysis are flawed, or 2)some of the concepts and principles underlying conventional analysis are flawed. If you approve, I suggest TA mathematics be discussed and compared to conventional approaches one concept and principle at a time.
I have never claimed that my approach or conclusions should be accepted because people don’t understand the mathematics involved. My position is, and has always been that the mathematics and approach I propose should not be rejected because some self proclaimed experts do not understand the mathematics involved.
The purpose of this site is to discuss/brainstorm ideas associated with information, complexity, and design. I believe the concepts and approach I am presenting are consistent with that purpose.
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warren_bergerson
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posted 19. February 2003 10:50
Rex,
Quote WB: As has been discussed here, it is easily shown using the automated assembly approach that 1)biological systems are extremely complex and 2)the processes needed to explain changes in these complex systems must have extremely powerful information processing capacity of the type described by TA's.
Quote RK: If it is easy, please do it instead of telling us that it is easy. If it were difficult, then it would make sense to not actually do it. But if it is easy, why not just do it and show the results instead of using "dead reckoning" to hypothesize what the answer would look like?
I am a bit confused by your question since all this has been discussed a number of times. Which part of the measurements don’t you agree with and why:
1. Automated self assembly of even a simple protein requires a very large number of assembly instructions.
2. Each assembly instruction has a high degree of complexity or improbability.
3. The complexity of a system is the product of the complexity of the individual assembly instructions.
4. This measure of complexity will be very large (well in excess of 10^10,000) for any multi-cellular organisms.
5. Even simple ‘evolutionary changes’ produced in a few generations by selective breeding will involve a very large number of changes in assembly instructions.
6. Any change in assembly instructions can be modeled by a TA system.
7. Even simple evolutionary changes produced by selective breeding require very large quantities of variation-selection processing to model or simulate.
I can’t believe you are seriously questioning the mathematics described above, although I could be wrong. I believe you are arguing that there ‘may exist some unknown technique’ for modeling evolutionary change which might be compatible with a lower measure of complexity.
I believe you are arguing, like many who argue against Dembski’s measures of complexity, not that the measure is wrong, and not that you have a better measure, but that the measures are invalid because you (or an accepted peer review process) have not accepted the measures.
I have presented highly simplified partial assembly instruction models based on cell division instructions. These simplified models provide rough estimates of the minimum level of complexity in a biological systems and rough estimates of the minimum levels of processing needed to explain simple evolutionary changes.
These simple models and calculations do not ‘prove’ that biological systems and evolutionary change processes are as complex as the calculations suggest, but they provide a reasonably strong argument supporting the conclusion. If you or any supporters of Darwinian evolution want to provide a verifiable, well defined model showing that simple evolutionary changes can be explained by simple RM&NS processing you are welcome to try.
I may be misunderstanding your argument, but it appears you are claiming not that 1) I can demonstrate that your calculation is flawed and I have a better alternative measure of complexity, but that 2)I don’t have to accept your calculation (if for example it has not been published in a peer review journal). Again, I am trying to understand what part of the calculation you don’t understand or agree with?
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Evan
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posted 19. February 2003 11:08
Warren writes,
quote:
The TA system mathematics I have presented here is based on ‘simple’ mathematical concepts and principles which should, IMO, be comprehensible by anyone with a basic understanding of set theory, mathematical modeling, and computer simulation. Where you go with this basic type of mathematics once you move beyond basic concepts, is something even most mathematicians will have difficulty visualizing unless they actually begin to work with it.
This is the problem - I see no sign that Warren has "actually begin to work with" the mathematics that he sketches in extremely general detail. He offers very basic concepts (which people understand quite well even though Warren says they don't,) but he offers nothing which indicates that he has ever "worked with" the mathematics.
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Rex Kerr
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posted 19. February 2003 20:10
- You provide no data that indicates that assembly instructions are a useful way to describe, say, protein folding.
- Protein folding according to the Poisson-Boltzmann equation isn't that complex (just computationally demanding to figure out the answer based on fairly simple equations).
- Only if the instructions are independent, which you have not shown.
- You do not provide a metric for computing complexity.
- Depending on what you mean by "assembly instruction" it is true that selective breeding can select a small subset of "assembly instructions" present in the initial population.
- Agreed. But you have not provided examples that demonstrate that modeling changes in assembly instructions with TAs is useful.
- In one generation, selective breeding can produce a population of, say, humans who only have blond hair, blue eyes, and are red-green colorbind. This is easily modeled by one iteration of a genetic algorithm. This isn't what I would consider "very large quantities of variation-selection processing".
quote:
Again, I am trying to understand what part of the calculation you don't understand or agree with?
It's the lack of anything that could sensibly be called a 'calculation' that is a problem.
This is not a calculation: "It seems obvious and easy to show that a rare recessive lethal gene will disappear from a population very rapidly."
This is a calculation: "Suppose that a recessive lethal allele of a gene appears with frequency f and is uniformly distributed throughout a population such that the frequency of carriers (heterozygotes) is 2f(1-f) (and frequency of dead individuals is f^2). Then after one generation the allele frequency will be: homozygote wild-type x homozygote w.t. p=(1-f)^4, genotype=wt ; w.t. x carrier p=4(1-f)^3*f , genotype = 1/2 wt, 1/2 carrier ; carrier x carrier p=4(1-f)^2*f^2 , genotype = 1/4 lethal 1/2 carrier 1/4 wt. Thus the frequency of dead individuals in the next generation will be (1-f^2)*f^2 / ((1-f)^4+4(1-f)^3*f+4(1-f^2)*f^2) = f^2 / ((1-f)^2 + 4f(1-f) + 4f^2) = f^2/(1+f)^2 ~= f^2*(1-2f). A rare allele has f small, so (1-2f) is close to 1, and the allele's frequency will change little from generation to generation."
You have done the former. I would like to see something more like the latter. Note that in this case, I have also illustrated that actually doing the calculation can lead to surprising results. A recessive lethal gene isn't rapidly lost from a population. (Upon further reflection, this isn't so surprising; only when you have two recessive copies does selection act, and it is very improbable to have *two* copies of that rare allele).
Anyway, since the thread is closing, this will be my last post in this thread, and also on this topic even if new threads are opened, at least for a couple of months. We've covered it in enough detail for now.
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warren_bergerson
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posted 20. February 2003 09:08
Rex,
Quote: 1. You provide no data that indicates that assembly instructions are a useful way to describe, say, protein folding.
Automated assembly instructions provides a verifiable method of quantifying the complexity of a protein and a quantifiable method of determining how much processing is required to change from the assembly of one protein to an assembly of another protein. A verifiable techniques for quantifying complexity would appear, based on basic scientific principles, to the absence of a verifiable techniques for measuring both 1)the complexity of proteins and 2)the complexity of the change process.
You might legitimately propose an alternative method of quantifying complexity of change process and argue that you proposed technique is either better or more reliable. You can argue and demonstrate that the calculation produces misleading values. You can not, however, legitimately argue that the absence of ability to quantify is inherently superior.
Quote 2: Protein folding according to the Poisson-Boltzmann equation isn't that complex (just computationally demanding to figure out the answer based on fairly simple equations).
As I understand it, scientists do have the ability to assembly some bio-chemicals under some limited conditions. It would therefore probably be possible to automate some such assemblies under controlled conditions. These automated process may not appear intuitively complex, but based on the definitions provided the complexity values become very large, very fast.
Quote : 3. Only if the instructions are independent, which you have not shown.
The automated assembly instruction technique eliminates duplicate or redundant instructions. The ability to address the issue of the independence of instructions is one of the benefits of the approach being proposed.
Quote : You do not provide a metric for computing complexity.
The complexity of an individual instructions is the ratio (total forms an instruction can take) to (forms the instruction can take that will result in a successful assembly). Total complexity of an assembly is the product of the complexity of the individual instructions. A very straight forward calculation. Numbers it will be recognized get very large very fast.
In many applications, the purpose of measuring complexity is to develop a lower bound estimate of the complexity. It is easy, even trivial to show that the assembly instruction complexity of a multi-celluar organism is much greater than, for example, 10^10,0000.
Quote: 5. Depending on what you mean by "assembly instruction" it is true that selective breeding can select a small subset of "assembly instructions" present in the initial population.
Selective breeding in a very few generations can produce ‘simple’ changes like changes in size. It is possible in a few generations to produce individuals which are bigger than any of the individuals in the initial population. In terms of human perception, bigger is a ‘simple’ concept. In terms of automated assembly, making a ‘bigger’ version is far more complex. This is particularly true when it is recognized that all sorts of complex adjustments are needed to make the bigger or smaller version work.
Quote: 6. Agreed. But you have not provided examples that demonstrate that modeling changes in assembly instructions with TAs is useful.
I have shown that the observed complex change can be modeled by complex information processing. If I can then demonstrate the existence within the biological system of processes which are logically equivalent to the processing performed by the TA then I have produced a logical model/explanation of how the change occurred.
We didn’t have time to discuss how one demonstrates that the logical equivalent of ‘each operation performed by a TA’ can be performed by a biological system. That will have to be a subject for a latter thread.
Quote: 7. In one generation, selective breeding can produce a population of, say, humans who only have blond hair, blue eyes, and are red-green colorbind. This is easily modeled by one iteration of a genetic algorithm. This isn't what I would consider "very large quantities of variation-selection processing".
Also not relevant to the discussion. Picking two Great Danes out of a population of dogs, or two eagles out of a population of birds is not selective breeding.
As this discussion closes let me say that while I obviously don’t agree with you on many issues, I respect the fact that you have been both willing and able to actually address the issues being discussed.
As I read your comments, your basic objection to what is being proposed is ‘It can not lead to useful results?". This in my view is always the ultimate question in science. On an intuitive basis, it is hard to accept an approach that estimates the complexity of an organism as being in excess of 10^1,000,000. It must be even harder to accept the possibility that these same organisms, starting from a single cell, have the computing capacity to generate/create complexity in excess of 10^1,000,000. This approach must be even more difficult to understand when we have loads of experts claiming that ‘the evolution of biological organisms can be explained by a one cycle per life time information processing process.
If there is a lesson to be learned from this thread, and I believe there is, then it is that the discussion was a debate between -1)automated assembly- a process that provides techniques for a)quantify complexity and quantifying the information processing needed to change complexity and techniques for b)modeling an type of evolutionary/adaptive change and 2)conventional biology/genetics- a process that offers not methodology for quantifying complexity and information processing and which claims evolutionary change is too complex to be modeled.
Finally, I would like to thank you for pointing out one of the interesting weaknesses in practical applications of GA models. GA models of often sited to demonstrate that simple variation-selection models can generate complex designs. TA mathematics, and much of the analysis with GA systems, would suggest that simple variation selection processes should have very limited, very primitive design capabilities.
You provided part of the explanation by pointing out that business applications of GA’s use non-random search. But non-random search works by limiting the search area. This approach is only effective if the solution you are looking for is in the limited search area. The only way a GA system could know to look in a limited area is if the programmers provided this information. If your observation is correct, and I believe RBH confirmed it, then GA’s are far less effective ‘design generators’ than is suggested by the literature.
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RBH
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posted 20. February 2003 10:36
warren wrote quote:
You [Rex Kerr] provided part of the explanation by pointing out that business applications of GA's use non-random search. But non-random search works by limiting the search area. This approach is only effective if the solution you are looking for is in the limited search area. The only way a GA system could know to look in a limited area is if the programmers provided this information. If your observation is correct, and I believe RBH confirmed it, then GA's are far less effective 'design generators' than is suggested by the literature.
No, RBH didn't confirm it, at least not in the form that warren generalizes in the last sentence of the quotation. GAs are used in practical search applications, and in that use the programmer does supply a fitness function, a definition of what is fit and what is unfit. The GA searches in the space of possibilities defined by the variables the programmer deems relevant.
However (and this is an important "however"), the use of GAs in testing conjectures and hypotheses in evolutionary biology is different from their use in applied search problems. And the structure of the GAs used in simulation research in evolutionary biology is different in ways I'm not going to waste my time explaining. A good deal of research on biologically relevant hypotheses is done using GAs: see this site for some references.
Moreover, GAs are being studied as design engines, and have shown that they can in fact produce novel and creative solutions to interesting problems. See this page for an entrance to some of that literature.
The bottom line is that regardless of whether TA is or is not a useful addition to the research armamentarium (and we still can't tell whether it is), warren's critique of current evolutionary biology and the use of GAs as research tools in evolutionary biology is badly mistaken.
This is the last time I will participate in a thread warren starts unless and until there is a clear demonstration that he has carefully studied the literature that he criticizes so freely.
RBH
[ 20. February 2003, 10:39: Message edited by: RBH ]
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warren_bergerson
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posted 21. February 2003 16:31
Quote RBH: Moreover, GAs are being studied as design engines, and have shown that they can in fact produce novel and creative solutions to interesting problems. See this page for an entrance to some of that literature.
Many individuals, it appears, believe that neo-Darwinian theory has the ability to explain simple evolutionary changes because GA systems, it appears, have the ability to generate some relatively simple designs. Most people apparently are not aware that the ‘design capabilities’ of the GAs are for the most part an illusion.
When you strip away the statistical and population rhetoric, a GA is a simple trial and error search engine. Such an engine even with very strong selection processes can only search a very small set of possibilities even over a large number of generations.
The GA search engine searches for the maximum fitness value from a fitness landscape. The fitness landscape is not calculated by the GA program, but by the developer or programmer of the GA. Because the fitness landscape is an input item, the developer knows, or can determine where the maximum fitness value is located. The programmer can, and apparently frequently does, help the GA program find the maximum fitness value by introducing a non-random or directed search routine. In the absence of either a directed or non-random search routine (or a multiple selection per lifetime mechanisms) a GA would produce only very elementary designs.
The same situation would exist for evolutionary processes based on random variation and natural selection. In the absence of directed or non-random design processes, organism would be only be able to find adaptive solutions to the most elementary of design problems.
Despite what some people may suggest, the issue here, IMO, is not the use of non-random searches to create the impression of design capability. The issue is treatment of the issue by the peer review literature. It appears from the lists provided by RBH that it is not difficult to get a paper published which suggests that a GA has produced a complex design. It is apparently much more difficult, given the relative absence of such papers, to publish a paper describing or addressing the impact of selecting non-random search processes.
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gedanken
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posted 21. February 2003 22:09
quote:
The GA search engine searches for the maximum fitness value from a fitness landscape. The fitness landscape is not calculated by the GA program, but by the developer or programmer of the GA. Because the fitness landscape is an input item, the developer knows, or can determine where the maximum fitness value is located. The programmer can, and apparently frequently does, help the GA program find the maximum fitness value by introducing a non-random or directed search routine. In the absence of either a directed or non-random search routine (or a multiple selection per lifetime mechanisms) a GA would produce only very elementary designs.
This is the same mistake that seems to be presented in multiple threads by multiple persons.
RBH and others have already answered this claim. But the basics of the problem is that there are GAs that are used for AI or other purposes, and there are GAs that are used for modeling evolution. Even the GAs that are used to model an aspect of evolution might introduce limitations and cannot represent the entirety of evolutionary processes, and are necessarily an abstraction.
That said, Warren’s claim about the lack of capabilities of the GA were based not on the actual outputs that can be observed, but on a claim of “displacement” (as Dembski uses the term) to the programmer. But to the extent that the GA is a model of the real world, then the “displacement” is to the actual characteristics of the real world, not of intentions by the programmer.
But of course this claim can be leveled about every program, that it only does what the programmer programs. That’s not really saying anything. What is significant is when the programmer does not actually understand what the output will be implied by the program that was written.
The argument really has two parts:
1) That the program was written by the programmer, and thus does only what was programmed. If this were in itself a criticism of the GA (or of any other model), then it would be a criticism of every model created in every science. We could argue that the mathematical pathway of a planetary orbital cannot be real science, because that pathway was calculated by the intention of the writer of the mathematical model. It is a non sequitur.
(“The fitness landscape is not calculated by the GA program, but by the developer or programmer of the GA.” The planetary path is not calculated by the mathematical formula, but by the developer of the formula?)
2) That the program has extra help that is not an accurate model of reality in order for it to produce interesting results. Only programs that have this additional input, not part of accurate modeling of reality, will produce the interesting and innovative result. No denial is made that a program will produce innovative result, just that in order to do so it must involve something that is an inaccurate representation of reality.
This second point has not been supported by Warren, is is simply an assertion. I would suspect that scientists have done a pretty good job of demonstrating that the design inputs to the GAs are fairly accurate representations of the parts of reality that they are modeling. I will leave this to others to give any specific cases, and ask of Warren to demonstrate his case in some more concrete way than just giving a wild assertion.
quote:
It appears from the lists provided by RBH that it is not difficult to get a paper published which suggests that a GA has produced a complex design. It is apparently much more difficult, given the relative absence of such papers, to publish a paper describing or addressing the impact of selecting non-random search processes.
But once again, the GA is not a “random search” process, it has a random component. (The role of “selection” is very significant, and that selection is modeled as a constraint of the real world in any sort of evolution simulation. That selection constrains the search in ways that are far from random. And the new individual states are only generated from previous states that passed selection, and are generated by both random and combinational techniques in most GAs. Once again far from “random search”. And RBH shows over and over that evolution is not properly modeled as a “search”, but rather a description of what happens when the constrained random processes of descent with modification meet up with for the most part non-random selection processes.) Every paper on the GA is about the impact of non-random “search” processes. If no such papers are published, then no papers would be published on GAs at all.
I think that I should not continue to reply, because things that have been explained pages before seem to become ignored or forgotten. I think that perhaps the arguments presented may appear more meaningful if the argument against them appear several pages back or in the last thread on similar topics where the reader may not notice, rather than just previously.
[ 21. February 2003, 23:07: Message edited by: gedanken ]
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RBH
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posted 22. February 2003 00:25
I understand now why warren's critique of GAs, and of evolutionary processes in general, has seemed so strange to me. warren wrote (the same quotation used by gedanken): quote:
The GA search engine searches for the maximum fitness value from a fitness landscape. The fitness landscape is not calculated by the GA program, but by the developer or programmer of the GA. Because the fitness landscape is an input item, the developer knows, or can determine where the maximum fitness value is located. The programmer can, and apparently frequently does, help the GA program find the maximum fitness value by introducing a non-random or directed search routine. In the absence of either a directed or non-random search routine (or a multiple selection per lifetime mechanisms) a GA would produce only very elementary designs.
I'll try just this once more. Some of it will echo gedanken's points. Four of the five sentences in that quotation contain major misconceptions or serious errors of fact. Only the first sentence comes fairly close to being accurate, and even it contains a confusion.
1. A GA used in an applied problem employs a fitness function (not "landscape") supplied by the developer, since the fitness function defines 'goodness' in the terms specified by the problem to be solved (and by the client) and the developer is being paid to find a solution in those terms. Given a fitness function, which is an equation that calculates a fitness value for each phenotype the GA generates, each evolutionary operator induces a different fitness landscape, and the GA searches on all of them simultaneously. Given two evolutionary operators, e.g.point mutation and crossover mating, a GA will simultaneously seach on two different fitness landscapes with different topologies. More evolutionary operators induce more fitness landscapes from the same fitness function. The fitness landscape is not an "input item." It is induced by the interaction of a fitness function and an evolutionary operator.
2. For warren to assert that "the developer knows, or can determine where the maximum fitness value is located" is simply bizarre. If the developer knew where the maximum fitness value is located he wouldn't bother to code the GA. He'd just write down the location and its fitness, send them (along with a bill) to the client, and not bother with all that pesky coding.
That quoted remark demonstrates more than anything else that warren's critique of GAs, and of evolution as a general process, is based on a wholly erroneous conception of what evolution is and how it is used in applied search problems. In fact, in applied problems of any interest, one has not the faintest idea what the topologies of the multiple fitness landscapes look like, say nothing of knowing where the maxima are. The GAs my firm employs search multiple hyper-landscapes of up to 72 dimensions each with on the order of 10^72 "locations" each. To suppose that the developer knows where the maxima are in those spaces is ludicrous. We now know a little bit about the topologies of those landscapes (notably that useful local optima actually exist) because the behavior of the GAs has provided some data about them, but humans have no way of knowing where the maxima in the spaces are short of employing the GA.
3. The only "non-random or directed search routine" in a GA is differential reproduction as a function of fitness - selection! Does warren imagine that a GA uses purely stochastic search? GAs (and evolution in biology) employ selection based on the local topology of the several fitness landscapes to produce non-random outcomes from random variability in populations. As a consequence, GAs can indeed produce novel designs that are so far from "elementary" that even the developers of the hardware evolution program I referred to above do not understand how the evolved circuits accomplish their function.
4. GAs used in research on biological questions are different from those used to solve applied search problems. As gedanken pointed out, GAs used in research on hypotheses and conjectures about biology are abstractions from the real world. A model is by definition - and intent - an abstraction in which one attempts to represent just those variables that are suggested by theory as relevant. One observes the behavior of the model and compares it to the behavior of the real system in the real world to assess the veridicality of the model and to test the theory that guided its construction. Models are never complete - a complete model would be a point-to-point mapping of the whole system in the real world. A model is a condensation, in a sense, of the real system. Typically, evolutionary algorithms used in biological research do not have an artificial or arbitrary programmer-supplied fitness function. Fitness in those programs is typically defined as reproductive success, as it is in nature. It emerges from the theory being modeled, not from the whim of the programmer.
5. As gedanken also pointed out, warren's claim that such programs cannot produce novel or innovative behaviors is merely a bald assertion unsupported by any data or reasoning. But in fact, such programs surprise their programmers regularly. Whether the innovations they produce are a product of the internal dynamics of the evolutionary process or are displaced to the external environment (and those two factors interact to produce the outcomes), evolutionary algorithms generate novel and unexpected behavior that is nevertheless appropriate to their selective circumstances. I don't know a better definition of "innovative."
I differ from gedanken in one respect. I won't ask warren to demonstrate his case. His representation of GAs as they are used in both search applications and in research on biological processes is so badly distorted that any "demonstration" he might provide will inevitably be fatally flawed.
Now I quit.
RBH
[ 22. February 2003, 00:34: Message edited by: RBH ]
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