Evolution and the NFL theorems

_{Mark

December 30, 2007

Intelligent Design}

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Ronald Meester CLICK HERE FOR THE PAPER Department of Mathematics, VU-University Amsterdam,

“William Dembski (2002) claimed that the NoFreeLunch-theorems from op-
timization theory render Darwinian biological evolution impossible. I
argue that the NFL-theorems should be interpreted not in the sense that the models can be used to draw any conclusion about the real biological evolution (and certainly not about any design inference), but in the sense that it allows us to interpret computer simulations of evolutionary processes. I will argue that we learn very little, if anything at all, about biological evolution from simulations. This position is in stark contrast with certain claims in the literature.”

This paper is wonderful! Will it be published? It vindicates what Prof Dembski has been saying all the time whilst sounding like it does not.

“This does not imply that I defend ID in any way; I would like to emphasise this from the outset.”

I love the main useful quote it is a gem!

“I will argue now that simulations of evolutionary processes only demonstrate good programming skills – not much more. In particular, simulations add very little, if anything at all, to our understanding of “real” evolutionary processes.”

“If one wants to argue that there need not be any design in nature, then it is hardly convincing that one argues by showing how a well-designed algorithm behaves as real life is supposed to do.”

Comments

In the case of, say, chaotic turbulence at the trailing edge of an airplane wing, the simulation never replicates measurements taken on an actual wing. That is, you cannot enter measured initial conditions of turbulent flow into a CFD simulator, set the simulator running, and then use the simulation to predict subsequent measurements. I believe I am saying for the third time in this thread that the trajectory of the simulated system will diverge exponentially from that of the actual system. So why do they use these simulations?tribune7_{January 2, 2008
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kairos: "Your hint is certainly true and this does invalidate the Hagg. argument but I have argued that his starting point (7) is not valid." (7) seems to be no more than an interpretation of what Dembski argues in NFL about blind searches and uniform distributions. What do you see wrong with it. The point I've picked up on in Haggstrom's paper is where he says: ".....Dembski's NFL argument would still pose an interesting challenge to evolutionary biology provided that empirical evidence shows that the true fitness landscape is similar to what one would expect to see under assumption (7)." Haggstrom goes wrong is in his either/or take on mutation rates. His logic seems to be that the mutation rate being what it is, renders (7) inconsistent with our knowledge of biology, that it would require the death of any organism experiencing any kind of simple nucleotide mutation at all. He seems unaware that protein space is composed of two kinds of subspaces depending on the importance of the protein's function at any particular a.a. position along its length; i.e., some portions of the protein length are susceptible to 'neutral' mutations, and others are not. The calculation I made was to show that if only 40% of the protein length is constrained by function, then, in the case of the malarial protein PfCRT, we have empirical evidence that the "Darwinian algorithm A" (which means 'reproduction-mutation-selection') in action only permits, at most, the change of two a.a.s despite a huge number of 'reproductions' or the organism. The probability of an a.a. substitution for the PfCRT works out to be less than 1 in 10^150, science's own UPB. This, then, implies that 'fitness landscapes' in nature really do fall of the edge of the table. Thus, per Haggstrom, Dembski's NFL argument poses an "interesting challenge to evolutionary biology?. Sometime back, someone at Panda's Thumb was arguing against Dembski using data from protein studies that showed permissible substitution rates at important functional points of the protein sequence to be of the order--this is strictly from a very flawed memory--10^-84. It was argued that this was below Dembski's UPB of 10^-150. This, nevertheless, is again a very steep 'fitness function'. Imagine two proteins being needed for a particular cellular function. Behe tells us that generally protein clusters of 6-10 proteins are needed for the performance of any cellular function. The probability of this cellular function coming about by "blind chance", using the 10^84, would then minimally be 10^-504. Thus the 'fitness function' for this real-life cellular function would fall off almost exactly along the lines that Haggstrom suggests is biologically unreasonable. His biology is wrong. But his math, together with what we now know about the malarial parasite and from protein studies validate the use of uniform distributions, thus validating Dembski's NFL argument. As I said: "Game. Set. Match."PaV_{January 2, 2008
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semiotic 007
You’re engaged in the logical fallacy known as appeal to authority.
Are you sure?
Would you care to quote their argument in support of this conclusion? You won’t find it.
Are you sure? Really this is not the case. That citation is in a paper that is all dedicated to show how NFLT DO NOT hold in some coevolution cases, precisely when there's a champion. At the end of this paper Wolpert (who was DIRECTLY involved in the ID controversy in the 90's) do explicitly state that “in the typical coevolutionary scenarios encountered in biology, where there is no champion, the NFL theorems still hold.” Sorry for you but this appears to be the argument you were looking for. Come on. Haven't you anything better?
This is something the special-edition editors and reviewers let pass that they should not have. Last time I searched the web for the paper, I hit upon an early version that was quite different from the published version.
But was it different concerning this fact? If yes, please give reference; if not please don't use an argiment that doesn't matter.
I have a hunch that the reviewers called for many changes, and the little proclamation did not rise to threshold.
This can be your idea but it's not correct. Indeed, what you have called "little proclamation" is somethinh that is present both in the Abstract and in the body of the paper, which is a clear sign that it's a major statement. This is even more true starting from what you wrote before about Wolpert's ideas.
Wolpert had previously said the opposite, and had given a good argument here: […] neo-Darwinian evolution ... And recent results indicate that NFL results do not hold in co-evolution.
Indeed this WAS his OLD idea about, several years before the IEEE Trans paper on Dec. 2005.
Evidently he thought that the coevolutionary “free lunch” results he and Macready were developing would apply to biological evolution. My best guess is that the two lapsed into thinking NFL applied when they determined that their results on coevolution did not. But if you examine the argument, you can see that it is fine without the last sentence.
That the argument was fine is your idea. The new statement by Wolpert does suggest a very different scenario; initially he tought that the argument could be fine BECAUSE in coevolution things could have been different and free lunches could occur. But AFTER having found that this is true only in some cases, DIFFERENT from biological ones, he was forced to admit that he was wrong and NFLT still hold.
It includes elements of what Behe has said recently, and is similar to what English had said in 1996: ... And as Park said in GA-List discussion of NFL in 1995, almost all functions are “too big” for physical realization. Thus there were two arguments against the applicability of NFL results to real-world optimization before Wolpert and Macready published their first paper. Wolpert concurred with English later, but mysteriously changed his mind.
No, it's quite simpler, he did change his idea about and he did express so in the (new) paper. Both arguments (coevolution and dynamic fittness functions) are not sufficient to invalidate NFLT and Wolpert simply recognized this fact by writing: “in the typical coevolutionary scenarios encountered in biology, where there is no champion, the NFL theorems still hold.”kairos_{January 2, 2008
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Semiotic 007: "Biological evolutionary systems are...nonlinear dynamical systems, and you should not expect predictions of specific evolutionary pathways to come out of simulation models. This is not a shortcoming of evolutionary theory." I do understand the limitations of modelling nonlinear systems. I'm not looking for a model that demonstrates the evolution of any particular complex functional structure. The evolution of any kind of complex functional structure would do (using a nonteleological evolutionary process). Thanks for the link to the paper. I'll read it and let you know what I think.j_{January 2, 2008
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perlopp,
do you mean that Meester’s formulation differ from Wolpert and Macready’s?
I know the thread's gotten long. I pointed out in 22 that Meester's "Theorem 1 is implied by Wolpert and Macready’s Theorem 1, but is not logically equivalent to it." That is, the equality of the sums implies the equality of the averages, but not the converse. If your understanding of the NFL theorems is limited to the averages, you have little way of understanding important results that came along later. Meester does not understand.Semiotic 007_{January 2, 2008
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Bob O'H says,
So, if Meester is right, we can’t build an acceptable model, so we can’t calculate CSI correctly.
I always supposed that Dr. Dembski intended to use an analytic model, and not a simulation model, to obtain an upper bound on the probability of evolution of the bacterial flagellum. But I think Meester's argument would apply at least as well to analytic models. One thing that can be said for computation of CSI is that only an upper bound, not a precise estimate, of probability is required, and a loose bound might suffice.
A corollary of Meester’s argument is that the work being done by the EIL is irrelevant to biology. I’m not sure this is the best blog to be making that argument on.
Dr. Dembski understands better than Meester that modeling is a matter of abstraction. I find it bizarre that Meester suggests that simulation of evolution will not be of value unless it accounts for the process at the level of chemistry. That's like saying we can't simulate an apple falling from a tree unless we take quantum gravity into account.Semiotic 007_{January 2, 2008
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Gloppy,
But why don’t lips sweat? Show me an evolution model.
I suppose the Designer didn't want all kisses to be wet.Semiotic 007_{January 2, 2008
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Instead of dancing, how about actually presenting an argument showing how Darwin’s statement that “I mean by Nature, only the aggregate action and product of many laws, and by laws the sequence of events as ascertained by us” is wrong.
The dance was to spare you. Your quote of Darwin is utterly irrelevant to my remark that "competition in a bounded arena" is a more primitive concept than fitness. I am genuinely trying to understand your misunderstanding, and my best guess is that you simply do not understand the phrase. Here is an outstanding paper that not only ties "competition in a bounded arena" to neo-Darwinism, but also gets us (pretty please) on-topic: Notes on the Simulation of Evolution. The author, Wirt Atmar, earned a dual Ph.D. in electrical engineering and biology, and very few people are as qualified to comment as he.Semiotic 007_{January 2, 2008
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But why don't lips sweat? Show me an evolution model. GloppyGalapagos Finch_{January 2, 2008
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"If one wants to argue that there need not be any design in nature, then it is hardly convincing that one argues by showing how a well-designed algorithm behaves as real life is supposed to do." I just want to second that I think this is my favorite quote as well. I know little of the math involved, and admit to as much - but I personally think the more we learn about evolution, the more plausible it is to say 'One can certainly argue there's design in here'.nullasalus_{January 2, 2008
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j says,
With computational fluid dynamics, one can model aerodynamics in practically as much detail as one wishes, and it actually provides results that match reality. Show us the equivalent for Darwinian evolution.
It happens that I have sat with researchers who set up a National Science Foundation center for study of computational fluid dynamics, discussing computational requirements. You are quite wrong about "practically as much detail as one wishes." With high Reynolds numbers (complex nonlinear dynamics), you never can get enough detail. The guys I talked with did not feel a Connection Machine was powerful enough for their work. Furthermore, you are playing it fast and loose with the notion of "matching reality." In the case of, say, chaotic turbulence at the trailing edge of an airplane wing, the simulation never replicates measurements taken on an actual wing. That is, you cannot enter measured initial conditions of turbulent flow into a CFD simulator, set the simulator running, and then use the simulation to predict subsequent measurements. I believe I am saying for the third time in this thread that the trajectory of the simulated system will diverge exponentially from that of the actual system. There is most definitely nothing in CFD analogous to an answer to the question, "What is the probability that the flagellum evolves?" CFD simulations do not accurately predict nonlinear fluid flow in fine detail for more than a short time. To put things simply, they can predict what the flow will be like, but not precisely what it will be. This is a limitation intrinsic to modeling the "evolution" of nonlinear dynamical systems. Biological evolutionary systems are also nonlinear dynamical systems, and you should not expect predictions of specific evolutionary pathways to come out of simulation models. This is not a shortcoming of evolutionary theory. That said, work on biologically-relevant simulations of evolution has barely begun. Although such simulations go back fifty years, relatively few life scientists are interested in simulation. Most of the engineering-types who are interested in simulation of evolution do not know enough about evolutionary biology to come up with simulations the life scientists find interesting. The engineers and computer scientists tend to think they know a lot more about biological evolution than they actually do, and the life scientists are rarely interested in collaboration.Semiotic 007_{January 2, 2008
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In theory, theory and reality are the same. In reality, they're not. GloppyGalapagos Finch_{January 1, 2008
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semiotic That is, the only layout that is ever realized is one that did not exist when it was simulated. That's because the model has been benchmarked against reality. Once a model is verified against reality then it can be used to predict outcomes from a hypothetical initial state. Isn't it great how models work like that? Once we know that a model successfully predicts the flight characteristics of an aircraft that exists then we can initialize it with aircraft designs that don't yet exist and see how they perform before we commit to bending metal. If we validate the design using the model then build it and it performs in reality as the model predicted we gain even more confidence in our model. Modeling a factory floor is the same thing - we trust that the hypothetical factory in our model will work the same way in the real world. We also build roads this way. We put in our signals and lanes and speed limits and intersections and so forth then put anticipated simulated traffic on it and see how it flows. We can do this because we have tested our model against reality in the past and are confident it accurately models reality. If we hadn't tested it we might discover the hard way that it is flawed - perhaps it mistakenly presumes automobiles can make 90 degree turns at 60mph as long as the light is green or that they can accelerate/decelerate instantly or that driver reaction time is instantaneous. All sorts of mistakes can be lurking in untested models. Models of biological evolution are so unlike this they really aren't models at all in any practical way. DaveScot_{January 1, 2008
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davescot wrote "As far as we know creative evolution is no longer happening. " yes it is...by intelligent designersari-freedom_{January 1, 2008
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Bob No one really knows what’s happening in the evolution of life on Earth, Darwinist bluster notwithstanding. Sure we do. We know a massive amount of evolution happened in the prehistoric past and we know that, comparatively, virtually nothing has happened during recorded history. As far as we know creative evolution is no longer happening. That's the real problem with Darwinian evolution - it hasn't been observed. Now it could be that it's just too slow to observe but it could also be that it doesn't happen at all and evolution was driven by something other than chance & necessity. Either way it's unconfirmed - purely hypothetical.DaveScot_{January 1, 2008
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Semiotic (73): When you say that It is easy to see that the theorem states that two sums are equal, while Meester’s theorem (page 4) states that two averages are equal. do you mean that Meester's formulation differ from Wolpert and Macready's?perlopp_{January 1, 2008
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j re; a robotic bird We can build things that fly faster, farther, & higher than a bird but if we were REALLY good we could build an aircraft that repairs itself, replicates itself, flies itself, and consumes nothing but water and sunflower seeds in the process... :)DaveScot_{January 1, 2008
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j @ 67 -

I do not think it is reasonable to summarise the extremely complex biology (and chemistry, physiscs . . .) that is associated to the process, into a single search algorithm. There are no realistic models of evolution that render this approach reasonable, life is simply too complicated. Computing probabilities in a model is one thing, but for these computations to have any implication, the models had better be very good and accurate, and it is obvious that the various models do not live up to this requirement.
The second is really an indictment of Darwinian theory: No one really knows what’s happening in the evolution of life on Earth, Darwinist bluster notwithstanding. As I pointed out above, this is not a good argument to make. Remember that the calculation of CSI needs a model for the probability of "finding" the specified pattern. So, if Meester is right, we can't build an acceptable model, so we can't calculate CSI correctly. A corollary of Meester's argument is that the work being done by the EIL is irrelevant to biology. I'm not sure this is the best blog to be making that argument on. :-) BobBob O'H_{January 1, 2008
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Are you saying they don’t reflect real world results?. . . .No, Dave said that we had to know either initial or present conditions to model, and I gave some examples of important simulations I think if evo simulations reflected real world results they would be readily accepted.tribune7_{January 1, 2008
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“What I cannot create, I do not understand.” – Richard Feynman (1988) Semiotic 007: No one knows how to build a bird, but we understand how to fly, and we have learned principles of flight that hold for birds as well as helicopters. With computational fluid dynamics, one can model aerodynamics in practically as much detail as one wishes, and it actually provides results that match reality. Show us the equivalent for Darwinian evolution. There's no fundamental reason that a robotic bird couldn't be built. Unlike with Darwinian evolution, theoretical understanding isn't lacking, just time, money and effort. Semiotic 007: You may treat OOS like Darwinist scripture, cite chapter and verse, and then assert that any Darwinist believes as Darwin did in 1859 — fine with me. Darwin ascribed to Lamarckian evolution, you know. The last devout Darwinist died a very long time ago. Don’t you think it is just a tad silly to pull out a dictionary and parse a 150-year-old scientific text to determine what evolutionary theory really is? That’s the stuff of Biblical exegetics, not life science. The quote in question regards the heart of Darwinian theory, not some small detail that Darwin got wrong from his ignorance or imagination. Instead of dancing, how about actually presenting an argument showing how Darwin's statement that "I mean by Nature, only the aggregate action and product of many laws, and by laws the sequence of events as ascertained by us" is wrong. Tell us what nonteleological corrections or additions need to be made to get Darwinian evolution to work.j_{January 1, 2008
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DLH says,
Just a reminder of the severe discrimination against ID, and anyone remotely appearing to support ID or even publish results of experiments or modeling that could be construed to be supportive of ID - especially in the USA.
I've corresponded with some regents and the provost of Baylor University in support of academic freedom. If you review my comments on the paper, you'll see that I've said nothing in the "pro-ID / anti-ID" dimension. My efforts to prove mathematical results on search and to help people understand NFL span a number of years. It genuinely offends me to see someone who knows how to do math waltz in and make utterly bogus claims about NFL without bothering to do math (or even look into the math that's already been done). I realize that Meester gives you some juicy quotes. But the technical content of the paper is atrocious. Are the quotes worth so much to you that you are willing to champion garbage? Here is Wolpert and Macready's seminal No Free Lunch Theorems for Optimization from 1997. Theorem 1 is on the third page, early in Section III. It is easy to see that the theorem states that two sums are equal, while Meester's theorem (page 4) states that two averages are equal. It may be somewhat harder to see that when Wolpert and Macready treat "alignment" of algorithms and problems in Section IV, "A Geometric Perspective on the NFL Theorems," they anticipate and formalize what Meester has to say on page 8:
These remarks sound like very obvious remarks, and in a way they are. Once a search algorithm is more (or less, for that matter) efficient than what you expect from the NFL-theorems, it must be the case that you use a special choice, or a special class, of fitness functions. But at the same time, you must use a careful choice of the search algorithm which must have been tailored around your choice of (the class of) fitness functions.
However, it was established in 2000 that each search algorithm rapidly obtains a good value for almost all functions: Optimization Is Easy and Learning Is Hard in the Typical Function. That is, one need not "use a careful choice" -- algorithm design is generally pointless because almost all functions are algorithmically random. Google Scholar indicates that this paper has been cited at least 16 times in the technical literature. Am I making it more clear now that Meester is simply wrong? An arbitrary (undesigned) search algorithm almost always works well in theory. But the theory does not apply to practice, because algorithmically random functions, for which almost all algorithms work well, do not "fit" into the physical universe. To my knowledge, no one has gotten a handle on what theory does apply in practice. Perhaps some of you have heard the saying from mathematical logic, "From a false premise, conclude anything." No matter how much you like Meester's conclusions, the "reasoning" he uses to reach them is bogus.Semiotic 007_{January 1, 2008
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That's the basic problem. Evolutionary theory is undefined and can't be tested.ari-freedom_{January 1, 2008
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No one really knows what’s happening in the evolution of life on Earth, Darwinist bluster notwithstanding. __________ “What I cannot create, I do not understand.” – Richard Feynman (1988)
No one knows how to build a bird, but we understand how to fly, and we have learned principles of flight that hold for birds as well as helicopters.
Competition is defined by Merriam-Webster’s... So, technically, there is no competition in Darwinian theory.
You may treat OOS like Darwinist scripture, cite chapter and verse, and then assert that any Darwinist believes as Darwin did in 1859 -- fine with me. Darwin ascribed to Lamarckian evolution, you know. The last devout Darwinist died a very long time ago. Don't you think it is just a tad silly to pull out a dictionary and parse a 150-year-old scientific text to determine what evolutionary theory really is? That's the stuff of Biblical exegetics, not life science.Semiotic 007_{January 1, 2008
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Thus there were two arguments against the applicability of NFL results to real-world optimization...
Oops -- meant to say "biological evolution," not "real-world optimization."Semiotic 007_{January 1, 2008
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kairos says,
Moreover, in this sense I observe that both Haggstrom and Meester DID NOT cite what David Wolpert (who did invent NFLT) wrote in his paper on IEEE Transactions on Evolutionary Computation), Dec. 2005: “in the typical coevolutionary scenarios encountered in biology, where there is no champion, the NFL theorems still hold.” What about this?
You're engaged in the logical fallacy known as appeal to authority. Would you care to quote their argument in support of this conclusion? You won't find it. This is something the special-edition editors and reviewers let pass that they should not have. Last time I searched the web for the paper, I hit upon an early version that was quite different from the published version. I have a hunch that the reviewers called for many changes, and the little proclamation did not rise to threshold. Wolpert had previously said the opposite, and had given a good argument here:
[...] neo-Darwinian evolution of ecosystems does not involve a set of genomes all searching the same, fixed fitness function, the situation considered by the NFL theorems. Rather it is a co-evolutionary process. Roughly speaking, as each genome changes from one generation to the next, it modifies the surfaces that the other genomes are searching. And recent results indicate that NFL results do not hold in co-evolution.
Evidently he thought that the coevolutionary "free lunch" results he and Macready were developing would apply to biological evolution. My best guess is that the two lapsed into thinking NFL applied when they determined that their results on coevolution did not. But if you examine the argument, you can see that it is fine without the last sentence. It includes elements of what Behe has said recently, and is similar to what English had said in 1996:
Do the arguments of [NFL] contradict the evidence of remarkable adaptive mechanisms in biota? The question is meaningful only if one regards evolutionary adaptation as function optimization. Unfortunately, that model has not been validated. It is well known that biota are components of complex, dynamical ecosystems. Adaptive forces can change rapidly and nonlinearly, due in part to the fact that evolutionary adaptation is itself ecological change. In terms of function optimization, evaluation of points changes the fitness function.
"Everything new is made old again." And as Park said in GA-List discussion of NFL in 1995, almost all functions are "too big" for physical realization. Thus there were two arguments against the applicability of NFL results to real-world optimization before Wolpert and Macready published their first paper. Wolpert concurred with English later, but mysteriously changed his mind.Semiotic 007_{January 1, 2008
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My favorite quotes from the Meester paper:
If one wants to argue that there need not be any design in nature, then it is hardly convincing that one argues by showing how a well-designed algorithm behaves as real life is supposed to do.
and
I do not think it is reasonable to summarise the extremely complex biology (and chemistry, physiscs . . .) that is associated to the process, into a single search algorithm. There are no realistic models of evolution that render this approach reasonable, life is simply too complicated. Computing probabilities in a model is one thing, but for these computations to have any implication, the models had better be very good and accurate, and it is obvious that the various models do not live up to this requirement.
The second is really an indictment of Darwinian theory: No one really knows what's happening in the evolution of life on Earth, Darwinist bluster notwithstanding. __________ "What I cannot create, I do not understand." -- Richard Feynman (1988) __________ Semiotic 007: "By the way, fitness functions are not essential to evolutionary theory. Competition in a bounded arena is." In explaining what he meant by the term "natural selection", Darwin wrote:
I mean by Nature, only the aggregate action and product of many laws, and by laws the sequence of events as ascertained by us.
Thus, it's all just supposed to be the outworking of the laws of nature (including stochastic processes). Competition is defined by Merriam-Webster's as "active demand by two or more organisms or kinds of organisms for some environmental resource in short supply." So, technically, there is no competition in Darwinian theory. Competition ("active demand") implies goal-directedness, but in Darwinian theory, there is no goal. Darwin's use of the term in the Origin can only be considered metaphorical (just as his use of the term "natural selection" was). What would be needed to validate Darwinian theory is to abstract from "the sequence of events as ascertained by us" the "many [nonteleological] laws" that yield "endless forms most beautiful and most wonderful." It's approaching 150 years since Mr. Darwin wrote his book, and no one has done this yet. Why not? Throwing one's hand up in the air and say, "It's all just too complicated," is to concede defeat. And to make a model with a built-in purpose-driven competition of some sort, and proclaim that this is a model of Darwinian evolution, is bogus. If the only way to get evolution to happen is with purpose-driven rules, then this implies something about evolution in nature.j_{January 1, 2008
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Are you saying they don’t reflect real world results?
No, Dave said that we had to know either initial or present conditions to model, and I gave some examples of important simulations in which it is impossible to know those conditions with precision or certainty. Simulation models can take on many forms, and simulation results can be used in many ways -- some valid, and some invalid. If I had only my experience in simulation modeling of crops, manufacturing facilities, and human lifting motions to draw upon, my notion of modeling would be relatively limited. There's no substitute for reading (many) technical papers.Semiotic 007_{January 1, 2008
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DaveScot says,
It’s not a model or simulation unless there’s something in the real world to compare it against.
Are you aware that layouts of manufacturing facilities are commonly chosen on the basis of simulation results? That is, the only layout that is ever realized is one that did not exist when it was simulated. Also, modeled entities need not be as concrete as you seem to think. Flight is an abstract physical phenomenon, and there are several models of flight. When Michelangelo came up with the notion of a helicopter, he had implicitly formed a model of flight that corresponded to no particular physical object. He put the model to empirical test and validated it. He established that the "principles of flight" were not to be obtained merely by looking a birds. Evolution is also an abstraction. Avida, for instance, is intended to put "principles of evolution" to test. You may criticize the test, but that is the intent.
Look up the words “model” and “simulation” for Pete’s sake.
Done. Now you take a look at: model OR modeling "first principles" (758,000 hits) "chaotic system" OR "dynamical system" sensitivity "initial conditions" (131,000 hits) "chaotic system" OR "dynamical system" qualitative (69,900 hits) It is reasonable to use first-principles models to predict the behavior of physical entities that have yet to exist. Any model of a chaotic system will, over the long term, diverge exponentially from the modeled system. But a model may be valuable in capturing qualitative features of the modeled entity. I am not making this stuff up.Semiotic 007_{January 1, 2008
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PAV Your post has been displayed four or five times but, you know, repetita iuvant and this is certainly true when right ideas are the opposite NDE theory would like ... Your hint is certainly true and this does invalidate the Hagg. argument but I have argued that his starting point (7) is not valid. Happy new year to anybodykairos_{January 1, 2008
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you can do all the kata you want and show off your black belt in super tiger dragon ninja kung fu, unless you can continually test your skills against live resisting opponents, IOW, models that fail to replicate the real world ought not be taken seriously :-)tribune7_{January 1, 2008
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