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Author
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Topic: Nature Refutes ID?: The Evolutionary Origin of Complex Features
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Argon
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Member # 276
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posted 20. May 2003 12:27
RBH wrote:
quote:
(...) John [Bracht]has not yet supplied a calculation to show that his suggestion is plausible, say nothing of calculating the probability that 23 different lineages would each produce a different program capable of performing EQU in 50 evolutionary runs.
Good question.
Back on the sixth page of this topic, Kirk Durston said:
quote:
When I look at the simulation under discussion, the specified complexity of the results falls considerably short of 70 bits. That being the case, no ID is required, the simulation shows that no ID is required (ignoring, of course, the carefully designed virtual fitness landscape which is designed to produce the desired results with a probability approaching 1), and so I cannot see how the simulation is relevant to ID, or how it can show that IC systems (requiring more than 70 bits of information) can occur in nature.
I am interested in knowing how the specified complexity was calculated. Perhaps I'm a bit behind the times but I thought specified complexity, like irreducible complexity, was originally advertised as being determinable even in the absence of knowing the history of a system. If we used the "random assemblage" model like the one William Dembski employed in his demo with a bacterial flagella, what numbers would we get?
Also, if the simulation had only been performed once from a single population of digital "organisms", such that we wouldn't know if other routes were possible, would the specified complexity calculations yield a different result?
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RBH
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posted 20. May 2003 12:27
Once again warren makes the unsubstantiated claim that there are biological processes and structures that are supposed by biologists to have occurred by means of the mechanisms of evolution, but that developed at too high a rate for those mechanisms to plausibly account for them. Warren provides no substantiating data nor even a worked-out example. So my request to warren is to provide such an example.
In order to meet the criteria warren specifies, the example must
(a) be a biological process that biologists claim occurred by the mechanisms of evolution, but that
(b) occurred (emerged from a precursor substrate) too quickly for those mechanisms to have plausibly generated it given the empirically known range of rates at which those mechanisms have been observed to operate in real biological systems.
That's a simple request, one which should not be difficult to meet since warren tells us quote:
Given the known complexity of biological systems, given the speed with which certain types of complexity are known to have evolved (human intelligence would be a reasonable example), and given the demonstrated inefficiency of (non-modified) mutation and natural selection search routines, it would seem reasonable to suggest that evolutionary change is the result of some process other than mutation and natural selection.
warren suggests that human intelligence is a "reasonable example" of a complex biological function that developed too quickly for evolutionary processes to account for its appearance.
In order to evaluate that claim, a couple of questions must be answered. Just how quickly did it occur? What is the rate of cephalic increase over generations beyond which evolutionary processes, operating at the rates they are known to achieve, are too slow to account for the emergence of human intelligence? warren tells us he wants mathematically precise models; those models require taking into account the known data. What are the data to be accounted for, warren? Please give us an example in sufficient detail that we can evaluate it.
The data available from the paper under discussion (along with its Supplemental Information) offers an opportunity for warren to test his claim. The paths of the various lineages that evolved to perform EQU are consistent with the evolutionary hypothesis. The code is available, and the control files are easily modifiable. I suggest that warren download it (he can get version 1.3 for Windows if he doesn't have a Unix machine available for version 1.6; that would require more extensive modification of the control files), and implement these other search algorithms he refers to and evaluate their performance on the same task set for the evolutionary mechanisms in the original paper. That's the comparison he is asserting is relevant; let him test it. Hypothetical invocations of implausibility or impossibility are easy; the test, though, is in systematic research. The means are readily available to warren now; let him provide some actual research results to evaluate his claims.
RBH
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YZ2
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posted 20. May 2003 12:34
Perhaps my question was not fully understood.I think there are two ways of interpreting it. One way is what Warren has suggested, that it is an actual past event that has occurred before the appearance of EQU. That a systematic combination search is adopted, to combine current NAND programs and test whether it fits any selection function. EQU may not be known or the target from the evolutionary process. An example of a fitted selection function is what Micah has produced (so nicely I would say). It is a very fast evolutionary method, without the use of random mutations and natural selection. Of course during the whole process, the selection function(s) are fully involved. As suggested by Warren, there is currently no evidence to suggest that it could not happen this way.
The other interpretation is a way of analyzing the current EQU after it is formed, by looking at all the possible combinations of its parts. Since analyzing the number of combinations are still much faster than analyzing the generated combinations of mutations/natural selection. This is a quicker way of understanding the EQU. Basically we are evaluating the efficiency of paradigms in scientific enquiry.
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Micah Sparacio
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posted 20. May 2003 13:41
"the probability that 23 different lineages would each produce a different program capable of performing EQU in 50 evolutionary runs."
This is all so ridiculous. That many, even the programmers are impressed by the "23 different lineages." Dawkins' Weasel program did as much, unfortunately. It's all part of what I'll call the black box phenomena of non-trivial evolutionary simulations.
Pim commented a while ago on how the paper insisted that the path was not smooth and how it required moving up and down and all around and pretty things like that. Not going into detail, I'll comment that this is part of the "deceiving ourselves" by the black box phenomena. In fact, this would make a good paper on the aesthetics of science. "Why Dawkins' simulation makes us Puke: An appreciation of Lenski and Schneider"
I stand by my initial intuitions, this simulation was quite smooth and direct and unimpressive. Not much more than a prettily packaged WEASEL program.
Actually, I was fortunate enough to play around with an "in development" WEASEL program yesterday that brings in the black box phenomena through co-evolving landscapes, with unique genotypic lineages emerging every time, as well as a less than 100% success rate.
It speaks volumes, especially since it shows that even Dawkins' crappy project can be made to conform with our Darwinian aesthetic.
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Argon
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posted 20. May 2003 14:10
I think we all agree with the truism that evolutionary mechanisms can only create evolvable functions, regardless of whether we subjectively consider the routes "smooth" or "bumpy". Withholding judgement about the relative poopiness of any particular simulation for now, can we address the question of whether the derived EQU functions are IC or not? Are they specified or not? A significant question is whether evolutionary mechanisms can generate IC systems (apparently yes), or specified complexity (dependent on the pathway, apparently).
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RBH
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posted 20. May 2003 14:29
Micah wrote quote:
This is all so ridiculous. That many, even the programmers are impressed by the "23 different lineages." Dawkins' Weasel program did as much, unfortunately. It's all part of what I'll call the black box phenomena of non-trivial evolutionary simulations.
But the simulations in the paper under discussions are not "black boxes" as I understand that term. They're perfectly transparent, in fact. All the data from all the runs are dumped to disk and are available for analysis. I don't follow your 'black box' remarks at all.
My remark about the probabilities was specifically directed at John Bracht's suggestion that random shuffling could have done the job - he actually used the 'tornado in a junkyard' locution. That's a quantifiable claim, and I asked him to provide the quantities. I am not impressed by those sorts of claims made in the absence of actual calculations on available data.
In the absence of more information, it's impossible to understand what you mean about the "in development" WEASEL program. I'm not concerned with our "Darwinian aesthetic." I'm concerned with testing the various claims that are made about Darwinian (and non-Darwinian in warren's case) mechanisms of adaptation to dynamic and co-evolving selective environments.
RBH
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charlie d.
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posted 20. May 2003 15:40
quote:
I stand by my initial intuitions, this simulation was quite smooth and direct and unimpressive. Not much more than a prettily packaged WEASEL program.
Micah:
One thing is for sure: WEASEL-like programs would not allow intermediate drops in fitness, like AVIDA does. It may be many things, but certainly not a repackaged WEASEL program with a smooth fitness function all the way to the top.
Unless you mean something else - your posts reads a little "disconnected".
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Pim van Meurs
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posted 20. May 2003 17:29
Micah:Pim commented a while ago on how the paper insisted that the path was not smooth and how it required moving up and down and all around and pretty things like that. Not going into detail, I'll comment that this is part of the "deceiving ourselves" by the black box phenomena. In fact, this would make a good paper on the aesthetics of science. "Why Dawkins' simulation makes us Puke: An appreciation of Lenski and Schneider"
Micah, what part of the simulation do you consider a 'black box' phenomenon? I showed how one could calculate the fitness function from the two plots which indicates abrupt changes in fitness both upwards and downwards. There is no reason to compare Lenski et al's work with Dawkins' Weasel program. Dembski's Weasel program has a set goal, any step towards this goal is rewarded by a fitness increase, unlike this simulation.
Perhaps it may be helpful to delay this discussion until we can determine if according to the definition of IC, the EQU is IC or not or that we have to amend the definition to exclude any evolutionary paths?
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Micah Sparacio
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posted 20. May 2003 20:53
Just to clarify, the black box phenomenon is my attempt to articulate the way that, when we have enough going on in our computing system, we tend be more impressed by it than is warranted. I started using the term regarding neural networks and the way philosopher's of mind have been enamored with them without really understanding them. If you've got a fairly complex neural network it is hard to analyze exactly what's going on, and it is tempting to think that they are doing more than they really are.
Dawkins program is obviously irrelevant to us. However, the Lenski paper seems a lot more impressive, even before we understand the dynamics behind the system. Why? Because:
1. It doesn't reach the EQU function with 100% accuracy
2. The target is not the same as the Avida program in which it is instantiated (multiple realizations)
3. It discovered a better solution than the human mind (apparently)
4. No intermediate function is individually necessary.
5. etc.
The authors do a good job of highlighting these nice features, and of impressing us with what's going on.
Argon asked about EQU being IC. I'm not sure how to address this. Is the text to Hamlet IC? Is a star IC? Is a multiplication function IC?
Pim, there are reasons to compare the Lenski paper to Dawkins Weasel program. There may not be a specific target Avida program but there is a target function that we're looking for. Just the same, the Weasel program can be formulated so that you've got a co-evolving genotype and decryption system, which makes the two systems a whole lot more similar.
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Argon
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posted 20. May 2003 21:40
Micah writes:
quote:
Argon asked about EQU being IC. I'm not sure how to address this. Is the text to Hamlet IC? Is a star IC? Is a multiplication function IC?
For starters, one might consider more useful analogies.
I'm not saying you (Micah) should be capable of evaluating IC-ness. It's more of an open question to other readers.
One could try to address this using the criteria Behe or Dembski use to define IC systems. That has been the traditional approach and it is at least a reasonable place to begin. The "evolved" EDU function is a very simple system for which all the parameters are known and all the interactions can be rigorously evaluated. In short, it's an extremely tractable system for asking just such questions.
[ 20. May 2003, 21:41: Message edited by: Argon ]
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John Bracht
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posted 20. May 2003 22:14
Hi all,
Just to clarify, I never used the term "tornado in a junkyard" analogy to describe the Lenski et al simulation. In fact, I was making a very different point (one which apparently was not understood when I made it) about the double standards of Darwinists when it comes to programs with unrealistic assumptions: they scream and holler at "tornado in a junkyard" simulations, yet they accept the Lenski et al simulation with nary a peep. Yet the Lenski et al simulation is far more unrealistic than a tornado in a junkyard simulation. Why the lack of outcry?
This was my original point. Now it seems to have been mutated into something quite different, but I'm thinking it's an interesting question. Given all the building blocks of EQU (as the program has) and given a high mutation rate (as the program has), what is the probability that EQU will pop out just by chance? Apparently it's fairly low, since the program that didn't select for intermediate functions failed to generate EQU. I'd love to calculate the probability of EQU's arising by sheer chance but I'm afraid I don't have the requisite math/computer skills to do so. One complaint I had about the Lenski et al paper from the start is that they failed to do a detailed analysis of precisely what is required to get "EQU"--how precisely must the various NAND functions be interrelated, how many different ways of generating EQU are there, etc. In order to know what the probability of reaching the destination, we need to know in detail where that destination is, and how far it is from where we started. I don't have the mathematical skills to unweave the complex interrelationships between NAND and EQU. However, I'd almost pay someone else to do it, if you have the skills: how would we go about approaching this problem?
Furthermore, I'd love to answer this question (but again I can't due to lack of math skills): what is the amount of information provided by the intermediate selectable steps? It's clear the program needs help to generate EQU; that help is in the form of functional intermediates. How much help to they give? This should provide a way to estimate some sort of probability bound which distinguishes the information gap a Darwinian process can cross. The data is in the paper, but the ability to analyze the complex interrelationships between various simple and complex logic functions I lack.
I also want to point out something about the detrimental mutations that were observed in the simulation. Notice that these fitness-reducing alterations were ALWAYS followed in the next generation by a fitness-enhancing change. Why is this? Why weren't the detrimental mutations allowed to sit awhile, maybe take over the population, before a beneficial mutation occurred?
I propose the following. The detrimental changes probably occurred in organisms that were fairly "fit" relative to their peers. Hence, they have some "capital" to play with and can afford to temporarily reduce their fitness. But, if they are unfit for long, they will be eliminated from the population. I'm sure many organisms had detrimental alterations which occurred and were eliminated. These organisms will never show up as winners at the end of the simulation. So this implies that once a detrimental mutation occurs, an organism's clock is ticking. It better find a way to get more fit--fast--so it can avoid elimination. In a practical sense, a mutation in the next generation is probably the only way to avoid elimination.
So yes--the organisms occasionally underwent a detrimental mutation. But sometimes they were able to "save" the situation by coming up with an even better, beneficial mutation immediately thereafter. But that's a far cry from an organism wallowing around in the depths of sub-optimality for generations and generations before stumbling on something that works. It's not surprising that we can look back over the evolutionary history and see organisms that made extremely temporary forays into areas of reduced functionality, and then bounced right back up the fitness peak. This doesn't really provide a general mechanism for crossing non-functional valleys, because the organisms that stay in these valleys will quickly be eliminated.
Some other thoughts about RBH's proposed further experiments. I would love to see an experiment where NAND was not supplied at the beginning. Indeed, many of the functions seem pretty high-level and optimized for producing logic functions (like "compare the value in two registers to see if they're the same"). Can these instructions be broken down into simpler components that the program could play around with, to build up the instruction set itself?
Can we make the program generate complexity if the only thing rewarded is reproductive efficiency (as in real biology)? Or do we have to directly reward the EQU function (which has no direct tie-in with efficient reproduction)? Can we evolve other complex logic functions besides EQU without directly selecting them? What about 3-input logic functions--how much pre-optimization must go into a program that can evolve them?
It would be great to begin addressing these issues in further simulations.
John
[ 20. May 2003, 22:27: Message edited by: John Bracht ]
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Pim van Meurs
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posted 20. May 2003 23:16
John: If you study the lineage file you will notice that not always after fitness declined it increased again. Fitness does recover after large drops in fitness.
You say that Lenski et al's simulation is 'far more unrealistic than a tornado in the junkyard scenario' but how can a simulation which actually tries to model the effects of mutation AND selection be more unrealistic than one which expects chance to bring all components together in one big swoop.
The mutation rate might and one need to explore the effects of reduction in mutation rates but no mutation rates can be unrealistic when compared to the instantaneous mutation of all components in a tornado fashion.
I see some very interesting research topics here for ID but I am somewhat taken back by how hard it is to get some resolution on whether or not EQU is IC or not. Micah gives some examples of Hamlet (we can drop quite a few words and still understand its meaning), a multiplication (single component). Neither one seems to come close to the definition of IC but EQU seems like it does.
John is interested in the information generated by the intermediate steps. I believe that all the necessary data are there to calculate such information but my question would be how would this be different from intermediates in nature?
John asks Can we make the program generate complexity if the only thing rewarded is reproductive efficiency (as in real biology)
If EQU were to increase reproductive efficiency then surely this would be possible but remember this is a simulation.
But if anything else the work of Lenski and all may have generated some ID research to address questions raised by John.
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RBH
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posted 21. May 2003 00:14
I reread the relevant posting (posted 14. May 2003 11:28) that John made. I have trouble seeing his remarks there as anything but the argument that chance shuffling could produce the programs that performed EQU, i.e. a tornado in a junkyard: quote:
I just want to add one final thing to the debate about Behe's IC definition, etc. I think his original definition had an implicit complexity limit. This is all a probabilities game, and if given all the components of a complex system plus a high shuffling rate, chance alone can shuffle them around into something selectable (like EQU). The probability of that in this program is very high because of the unrealistic scenario the program embodies (and because of its failure to accurately model what biotic reality looks like). (Emphasis added)
That allegedly high probability of getting a program that performs EQU "given all the components of a complex system plus a high shuffling rate" is what I want to see. What is that probability, not (as John says in the quotation immediately below) the probability of the various evolutionary pathways.
In his most recent posting John shifts his argument from the probability of getting a program that performs EQU by shuffling around components to the question of the probability of the various evolutionary pathways by which such programs could evolve. quote:
One complaint I had about the Lenski et al paper from the start is that they failed to do a detailed analysis of precisely what is required to get "EQU"--how precisely must the various NAND functions be interrelated, how many different ways of generating EQU are there, etc. In order to know what the probability of reaching the destination, we need to know in detail where that destination is, and how far it is from where we started. I don't have the mathematical skills to unweave the complex interrelationships between NAND and EQU. However, I'd almost pay someone else to do it, if you have the skills: how would we go about approaching this problem?
But that's a quite different question. It is the reef on which I think all the IDist hoohah about probabilities in evolution founders. It embodies the notion that there is some single canonical 'NAND to EQU' path. But the simulation shows that's false. That was the object of the research: To see what some of those pathways might be. Given the open-endedness of the simulation (the programs could have evolved to as long as they 'wished' subject only to limitations of RAM in which to run), the number of potential pathways is (formally) infinite, so a pre-simulation description of what is "required" (beyond the shortest hand-written program the authors supplied) is impossible.
But that question is actually irrelevant given the definition of IC in terms of the present state of a structure or process. The 23 programs that evolved to perform EQU (and it's those programs that are relevant, not EQU itself as an abstract logic function) were all irreducibly complex by Behe's knockout criterion. So we know now that IC structures can evolve by Darwinian mechanisms, and can do so by multiple pathways.
Yet the impossibility of even one evolutionary pathway is what the Explanatory Filter and (specified complexity) must establish in order to eliminate regularity and calculate only the probability of assembly by chance in order to infer design. The onus is not upon evolutionary biologists to list all the potential paths and calculate their probabilities; it is Dembski's ahistorical analysis that must be justified by IDists. The paper under discussion shows that there are multiple pathways even in as simple a system as was simulated, and that even the shortest handwritten assembly language program that performs EQU is apparently two instructions longer than the shortest program that evolved. Contrary to Micah's remarks, those are striking results. An ID design detection program needs to consider now whether its assumption that the current state of a structure embodies the information necessary to infer design is tenable, and, if it shifts to an analysis of histories as John did above, whether its program of design detection is even feasible given the difficulty of identifying all potential evolutionary pathways.
RBH
Added in edit. John also wrote above quote:
So yes--the organisms occasionally underwent a detrimental mutation. But sometimes they were able to "save" the situation by coming up with an even better, beneficial mutation immediately thereafter. But that's a far cry from an organism wallowing around in the depths of sub-optimality for generations and generations before stumbling on something that works.
That's not quite accurate. They didn't necessarily come up with "an even better, beneficial mutation immediately thereafter." Look carefully at the definition of "step" in the paper. The "next" step in a series of mutational steps did not necessarily come in the next cycle of reproduction.
Finally (for this edit, anyway!) John asked quote:
Can we make the program generate complexity if the only thing rewarded is reproductive efficiency (as in real biology)?
But that's not what occurs in "real" biology. In real biology reproductive efficiency in a particular selective context is what is rewarded, not reproductive efficiency, period. If one does the latter (as I have done in Avida) one gets the shortest critters that can reproduce, and that's all. Absent selection on any other criterion, they evolve to be real reproductively efficient. And that's exactly what one would expect. What does John want? Spontaneous generation of logic functions absent any selection - environment-free evolution? That reflects a profound misunderstanding of real biology. Reproductive efficiency in a selective environment is exactly what was rewarded in the simulations in the paper under discussion, and that's like real biology, not environment-free reproduction.
RBH
[ 21. May 2003, 00:37: Message edited by: RBH ]
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John Bracht
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posted 21. May 2003 01:31
RBH,
Your last post was so confused that I just want to ask for clarification. At one moment you imply that I assume there's only one pathway to EQU--and the next, berate me for asking about multiple pathways! You seem to think I've shifted my argument (from asking about probabilities in general) to asking how we'd calculate the multi-pathway probability of getting EQU, when I see the latter as a way to get at the former . Indeed, I'm mystified why you set up the strawman argument that I'm assuming only one "NAND to EQU path", when I explicitly asked how we'd go about calculating the probability for the complex interrelationships between NAND and EQU, given the multiple possible solutions. But then, you get upset about whether it's IC, but I can't figure out how that ties in with all the rest of what you were arguing about. Perhaps you could settle on one or two issues that we could discuss (it'd be nice if they don't involve logically contradictory premises, too!).
Just so you remember that I didn't assume only one path:
quote:
One complaint I had about the Lenski et al paper from the start is that they failed to do a detailed analysis of precisely what is required to get "EQU"--how precisely must the various NAND functions be interrelated, how many different ways of generating EQU are there, etc.
Anyway, I'm not too concerned with all the above. I think you raise the crux of the matter when you state
quote:
But that's not what occurs in "real" biology. In real biology reproductive efficiency in a particular selective context is what is rewarded, not reproductive efficiency, period. If one does the latter (as I have done in Avida) one gets the shortest critters that can reproduce, and that's all. Absent selection on any other criterion, they evolve to be real reproductively efficient. And that's exactly what one would expect. What does John want? Spontaneous generation of logic functions absent any selection - environment-free evolution? That reflects a profound misunderstanding of real biology. Reproductive efficiency in a selective environment is exactly what was rewarded in the simulations in the paper under discussion, and that's like real biology, not environment-free reproduction.
This, at least, is conceptually clear. Here's the question I'd like answered: what in biology is ANYTHING like the EQU function selected for in this simulation? The rewarded critters can satisfy some esoteric "function" which has no real relevance to their reproductive efficiency (indeed, look at figure 3a from the paper to see that reproductive efficiency declines as the organisms evolve). In the real world, where organisms compete to reproduce better, these guys would be toast. All the authors have done is create a completely contrived "fitness function" that links what they want (in this case, EQU) to "fitness" (measured by SIPs awarded). I think it's RBH who has a profound misunderstanding about what the real selective pressures in biology are like. How does anything like EQU get tied to reproductive efficiency in real biology? It's not enough to just "want" it to occur or be convinced, deep in your heart of hearts that it does--you need to show how the sort of esoteric, arbitrary fitness function that rewards EQU simulates ANYTHING in real life. My point is this: Darwinian evolution is only concerned about ability to reproduce oneself. It doesn't reward fancy EQU functions or anything else that isn't immediately helpful in reproducing oneself. And nothing in the EQU function, intrinsically, helps one reproduce oneself. Indeed, most increases in biotic complexity do nothing intrinsically to help one reproduce oneself relative to a simpler organism (classical example: human, 20year life cycle, bacteria, 20 min. life cycle).
So how does EQU apply to real biology? What is the equivalent "selective environment" in the real world that might drive such an increase in complexity in real biology?
John
[ 21. May 2003, 01:36: Message edited by: John Bracht ]
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RBH
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posted 21. May 2003 02:50
John,
Your initial assertion about probabilities was quite specific. I'll quote it again: quote:
I just want to add one final thing to the debate about Behe's IC definition, etc. I think his original definition had an implicit complexity limit. This is all a probabilities game, and if given all the components of a complex system plus a high shuffling rate, chance alone can shuffle them around into something selectable (like EQU). The probability of that in this program is very high because of the unrealistic scenario the program embodies (and because of its failure to accurately model what biotic reality looks like). (Emphasis added)
You here say quite clearly that chance assembly processes were very likely to produce the 23 different programs that perform EQU. You made an implicitly quantitative assertion ("The probability ... is very high ...") and I asked you what that probability is.
In your recent posting, you shifted from asserting that the probability of chance assembly is very high to wondering about the probabilities associated with all the potential evolutionary pathways. That's what I contend is both irrelevant and impossible.
Whether EQU itself or a direct analogue of EQU is found in 'real' biology is, as charlie d pointed out several pages back, irrelevant. The paper did not set out to simulate a specific biological phenomenon; it set out to find out whether an outcome - an assembly language program that performs EQU - could be produced by regular evolutionary mechanisms in a context in which simpler logic functions were selectively advantageous. And the answer is 'yes.' Further, the programs that evolved were irreducibly complex as determined by Behe's operational definition, the knockout procedure. So we now know that irreducibly complex phenomena can be produced by evolutionary processes.
Nevertheless, there are biological phenomena that are analogues of certain logic operations and indeed of much more complex mathematical operations. For example, interactions among excitation and lateral inhibition in the processing of visual information in various organisms' peripheral visual systems perform the equivalent of the Laplacian of a Gaussian (LoG) operator. The selective environment that would drive the evolution of that capability is one in which high visual acuity is selectively advantageous. The principal 'raw materials' - primitives - necessary as precursors to evolving that capability are the existence of both excitatory and inhibitory synaptic connections and neural summation over space/time capability; in formal terms, affirmation and negation and integration. Those, in turn, derive from still more primitive cellular and biochemical processes that are ubiquitous in living organisms and need only be coopted under selective pressure. And as a whole lot of real biological research shows, cooption is also ubiquitous.
Other peripheral neural structures perform integration, differentiation, ANDing, ORing, and more complex combinations of those primitives. I'm not aware offhand whether EQU itself is performed (automatically by virtue of hardwiring) by one or another neural structure, either peripherally or centrally, but it wouldn't surprise me. So finding that an evolutionary process can create programs that perform EQU isn't completely irrelevant to biology.
RBH
[ 21. May 2003, 02:59: Message edited by: RBH ]
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