Uncommon Descent Serving The Intelligent Design Community

When Improbabilities Become Exponentially Improbable

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The first insight I had into the nonsensical nature of the random mutation (RM) part of the RM plus natural selection (NS) hypothesis came through my mathematical studies and experience in software engineering. See here for some probabilistic calculations about the most simple of all computer programs.

Of course, Darwinists always ask, How can you know that RM+NS can’t account for all of life? The answer is simple, and it’s called probabilistic combinatorics.

The underlying biochemical and information-driven functions of living systems are tightly integrated and controlled by an unimaginably complex, sophisticated, fault-tolerant, self-repairing, self-replicating computer program. Components of such a system cannot be altered to produce significant innovation without the simultaneous, coordinated alteration of the components with which they interact. This is what software engineers do, not copying errors.

This is a deafening cry of design.

A microbe did not mysteriously mutate into Mozart and his music, and most people, thankfully, are smart enough to figure out that this is a silly idea.

Comments
I am sure there is plenty ofphony math out there.John A. Davison
September 23, 2006
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John Davison, "Is not all of mathematics natural?" Theoretically. But in practice, I've found Numerical Analysis particularly unnatural. Or at least awkward.Douglas
September 23, 2006
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Salvador: "I was especially eager to hear what you had to say about the book given your background in science from Cornell." I'm not the person you are pointing to. I hold a PhD in Electronics and Computer science and I have never studied at Cornell.kairos
September 23, 2006
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Kairos, Thank you so much for your informative response. I was especially eager to hear what you had to say about the book given your background in science from Cornell. regards, Salvadorscordova
September 20, 2006
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John Davison:
Thanks for the plug PaV but Davison doesn’t have a “theory.” What he has is a new hypothesis which remains in complete accord with everything we know from the experimental laboratory and the fossil record.
Indeed, you're right! It is an hypothesis, and a good one at that. John Davison:
Everything in the world is natural or it wouldn’t be there. All things became natural when the Creator or Creators produced them. Is not all of mathematics natural? Does anyone still think that mathematics was the product of the human mind? Science is nothing but discovery of what has always been before us just waiting to be disclosed.
I couldn't agree with you more, John. The Pope, in Regnesburg, made it apparent that the way he plans to attack the tyranny of the sciences is to point out this very fact; that is, the world has a rational basis. (In physics you would call it Hilbert space.) And all scientific knowledge is possible only because of this rational basis is imposed, rather than being a product of nature itself. Hence, this rational basis implies its own creation, and so, reason leads us to "beingness", which, as the Pope points out and terms it, comes to us as a Christian/Hellenic inheritance. Thus, theology and philosophy--two disciplines that concern themselves with "beingness"--are rightly positioned before the human mind (our rational faculty). Excuse the prolix, but philosophy requires philosophy.PaV
September 19, 2006
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Tom English: I know the feeling, and can sympathize.PaV
September 19, 2006
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kairos and PaV, Sorry not to respond properly. I need desperately to get some work done.Tom English
September 19, 2006
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PaV Everything in the world is natural or it wouldn't be there. All things became natural when the Creator or Creators produced them. Is not all of mathematics natural? Does anyone still think that mathematics was the product of the human mind? Science is nothing but discovery of what has always been before us just waiting to be disclosed. As for evolution, it is FINISHED and has been for a long time. "Here I stand. I can do no otherwise." Martin Luther "A past evolution is undeniable, a present evolution undemonstrable." John A. DavisonJohn A. Davison
September 19, 2006
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#52 Salvador: "Have you had the chance to read Genetic Entropy yet? I would be curious to hear your comments. The issue is taht even if a functional protein formed, what’s the chance it will remain in that state to be any good. Yes, I read it last July (and I also wrote a short comment for Amazon). My opinion (I cite my comment) is that this book provides very good, clear and useful information about the real status of neodarwinian mechanism, mainly concerning the inadequacy of random mutation+selection to both repair genome degradation and macroevolution. Moreover in my opinion it is of particular importance that many nails used for the NDE coffin are provided directly by strict darwinian researchers such as Haldane and Kimura! My main criticism is that the author in some points has forced his (good) arguments to support a specific YEC position (actually the age of the first men). IMHO it would have been better to provide only the scientific arguments with their intrinsic strength. Anyway a very good work in my opinion. Note for #1 reviewer: it is not correct that the author does not consider duplication as a possibility for random evolution. Indeed, in his answers to objections at the end of the book, he explains why gene duplication does not theoretically improve the plausibility of the primary axiom.kairos
September 19, 2006
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Thanks for the plug PaV but Davison doesn't have a "theory." What he has is a new hypothesis which remains in complete accord with everything we know from the experimental laboratory and the fossil record. He also rejects special creation, divine intervention or any other device which denies reproductive continuity. Man is very definitely an animal as this and every other forum demonstrates beyond any reasonable doubt. "A past evolution is undeniable, a present evolution undemonstrable." John A. DavisonJohn A. Davison
September 19, 2006
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Tom English: "Knoll also indicates that between 800 million and 1.3 billion years passed between the appearance of the first eukaryotes and the appearance of eukaryotes clearly related to modern groups. Decide how many base pairs you want the genome to gain. Divide that number by 800 million years." I think all of this number-crunching shows how little we're able to use this information. For example, dividing by 800 million, the 8 billion base pairs we have amounts to 100 base pairs/yr. We could probably come up with all kinds of numbers---but how informative will they really be. "I’ll just give you a teaser: I suspect that in sexual reproduction the ovum contributes a considerable amount of information to the offspring. This is my only point of agreement with Jonathan Wells." I agree that the ovum contributes considerable information--in one of the most hard to read (impenetrable and boring come to mind) book ever written, What Genes Can't Do, Lenny Moss makes the fundamental contribution of cells (ovum) abundantly (and repetitively) clear--but this is no different than panspermia: it simply pushes the problem back. The problem then becomes where did the cell acquire this information? I don't see how this helps. Without much serious thought, I would think two mechanisms are available. One is "front-loading", which simply says that when cells came into existence the original chromosomes had all the information encoded to produce all of the abundant and diverse life we see, with chromosomal rearrangements (a la Davison's theory) and deletions resulting in the genomes we now see. This has a lot going for it. It certainly is tidy. The other mechanism is de novo "creation" of new genomes, at first representing producing kingdoms and phyla, and later producing the major classes we see, with simply chromosomal rearangements producing families of organisms, and adaptation bringing about genera and species and varieties. There are abundant theological problems with this (just ask the Creationists and, from the Catholic side, the Thomists), but this is consistent with, or at least applicable to, the work of "Wisdom"--a personified, but less than divine, power--that we read about in Wisdom literature. Darwinists, of course, would howl at this approach. (But I, of course, howl at what they have to say, so I guess that's a stand-off.) It might be virtually impossible to separate these two mechanisms from each other, OR, from a more naturalistic explanation as well. (God is humble. He stays hidden, and only reveals himself to the humble.) But to try and explain what we know of plants and animals, the fossil record, molecular biology, etc, etc. while invoking Darwinian mechanisms just can't be done. I don't think it will be too long before it all collapses. Well, just some musings.PaV
September 19, 2006
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Kairos, Glad to see you. Have you had the chance to read Genetic Entropy yet? I would be curious to hear your comments. The issue is taht even if a functional protein formed, what's the chance it will remain in that state to be any good. Salvadorscordova
September 19, 2006
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For all you chance-worshipping atheists out there, please document a single instance supporting random mutations as creative elements in any evolutionary sequence. While you are at it show me a single sexually reproducing animal that will ever become another species or that ever did in the past. After you have admitted that you can't, I have a few more things for you to concede as nothing more than figments of an overactive collective human imagination. Of course you will never admit that you can't because to do so means that your entire view of the living world is meaningless nonsense. I certainly don't expect anyone here to do what William Bateson did as I have documented both here and in hard copy. I refer you to the side board and my published paper "The blind alley: its significance for evolutionary theory." Neither Mendelian (sexually mediated) genetics nor allelic mutation nor natural selection ever had anything whatsoever to do with creative evolution except to ensure ultimate extinction. At that they have been superlative. "A fanatic is one who can't change his mind and won't change the subject." Winston Churchill Carry on with your fantasies. Don't pay any attention to me. At this point I wouldn't know how to handle it anyway. It is hard to believe isn't it? I love it so! "A past evolution is undeniable, a present evolution undemonstrable." John A. DavisonJohn A. Davison
September 19, 2006
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PaV, "I don’t understand why you’re making the distinction between “random” and “pseudo-random”. Can you predict the output of a rng?" The pseudo- truly is important in practice, though the question of whether anything is "really" random is philosophically deep. Cryptologists have cracked cryptosystems by exploiting predictability of pseudorandom number generators (PRNGs). The response has been to develop cryptographically secure PRNGs. They are harder to predict. "If you want a “real” random number generator, then why not use a Geiger-Counter and a radioactive source" That's what the HotBits web site does for you. See the link at post 17. PaV: "Eukaryotic life appeared over a relatively short period of time. Bacteria dominated up until shortly before the pre-Cambrian. Without bothering to go look at the numbers, off the top of my head, I would say that you have, at most, 3-400 million years to basically come up with the eukaryotic genome, which has billions of bases." Wiki: "Knoll (1992) suggests [the eukaryotes] developed approximately 1.6 - 2.1 billion years ago. Fossils that are clearly related to modern groups start appearing around 800 million years ago." So Knoll indicates that at least 1.4 billion years passed between the appearance of bacteria and the appearance of eukaryotes. The modern eukaryote S. pombe has just 14 million (not billion) base pairs. I take this as an upper bound on the number of base pairs in the first eukaryote. Dividing the latter quantity by the former gives one base pair per hundred years. Knoll also indicates that between 800 million and 1.3 billion years passed between the appearance of the first eukaryotes and the appearance of eukaryotes clearly related to modern groups. Decide how many base pairs you want the genome to gain. Divide that number by 800 million years. "Well, Tom, what’s your proposed mechanism?" Well, it's certainly not viruses from outer space. It's late. I'll just give you a teaser: I suspect that in sexual reproduction the ovum contributes a considerable amount of information to the offspring. This is my only point of agreement with Jonathan Wells.Tom English
September 19, 2006
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#47 "Thus the probability that a random permutation of 100 amino acids represents cytochrome C is 3.8 x 10 ^ -69. That’s a very low probability, but it is much greater than Bill Dembski’s universal probability bound of 10 ^ -120. Furthermore, there are supposedly many sequences of 100 amino acids that represent proteins other than cytochrome C." Let us (only for a moment) accept this computation as plausible. However 10^-69 is a probability enormously low and you cannot save your reasoning by simply observing that it is higher than Bill's UPB. First, this number is 10^-19 times the Borel's UPB (a quite sufficient number to declare something as pretty impossible). As the estimated universe time is about 10^17 seconds, this means that this level of probability can be reached by accumulating a sequence of dependent events, one for each second, with Borel probability during all the universe time. Are you realizing that value of your argument? "Note also that the human-designed protein chignolin has only 10 amino acid residues. This suggests to me that life could have started very small." Instead, the fact that in nature the smaller protein is very much larger suggests to me something completely different :-)kairos
September 19, 2006
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#35 "Evidently you have the Cambrian proliferation of body plans in mind. Due to the fact that gene expression is highly nonlinear (with genetic regulatory networks, protein interaction networks, and inter-cellular communication), small changes in genotype can account for big changes in phenotype. Provided we stick to complexity in the sense of Kolmogorov (algorithmic information, as I specified above), there’s no evidence to back up your claim." Tom you are completely reversing the burden of the proof. Actually there is no evidence at all that non-linearity in gene expression could be useful in finding the right path in phenotype evolution. In (good) science something that hasn't a decent chance to occur is discarded as a plausible explanation. Please prove before that your supposedly magic mechanism is able to get your claim and we'll discuss after. "The notion that larger populations search a fitness landscape better than smaller populations is a common misconception. Under various circumstances, a small population is more likely to escape a local maximum than is a large population." What are you saying? A small population simply provides much fewer tries in the space search and this produces a MUCH LESS capability to find decent solutions. Think to the genetic algorithms. “Almost all fitness functions are irregular in the extreme. That is, they are algorithmically random, and thus they are easy to optimize. Let’s say we uniformly draw a fitness function from the set of all functions from the space of genotypes to the set of all fitness values. Irrespective of the size of the space of genotypes, 916 fitness evaluations yield with 99.99% certainty a genotype that is more fit than 99% of the genotypes." Only when the search space has certain characteristics and aonly at the extreme; but you cannot argue in this sense for the biological search spaces. Simply, in the meantime you must accept that the search space is not reasonably affordable by RM+NSkairos
September 18, 2006
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PaV, Thanks for putting me onto cytochrome C. I am out of my depth here, but I have learned poking around the web that 3.8 x 10 ^ 61 of the 10 ^ 130 sequences of 100 amino acids represent cytochrome C (H. P. Yockey, 1977. On the Information Content of Cytochrome C. Journal of Theoretical Biology, 67: 345-76). Thus the probability that a random permutation of 100 amino acids represents cytochrome C is 3.8 x 10 ^ -69. That's a very low probability, but it is much greater than Bill Dembski's universal probability bound of 10 ^ -120. Furthermore, there are supposedly many sequences of 100 amino acids that represent proteins other than cytochrome C. Note also that the human-designed protein chignolin has only 10 amino acid residues. This suggests to me that life could have started very small. "Would you like to explain where the extra 16 mutations came from?" Data dredging. (Wiki has a disappointing article on the topic.) You might as well ask me to account for the long regions with no mutations. The researcher, Katherine Pollard, had a computer plow through the human and chimp genomes to find regions with substantial differences. She identified 49 "human accelerated regions" (HARs). What makes HAR1 number one is that it is, as Pollard points out, "really an extreme case." http://www.sciam.com/article.cfm?chanID=sa003&articleID=00023D61-9116-14E3-911683414B7F0000 So what I am saying is that if you slide a window over two sequences of 3 billion base pairs looking for anomalous regions, find 49 of them, and then report the very most anomalous, it really is going to look anomalous. All base pairs have been mutated many times in both species in the past six million years. The question is what happened in humans that allowed mutations in HAR1 to be adaptive when they are lethal in chimps and many other species. My uneducated guess is that what ultimately accounts for the high mutability in HAR1 is some prior mutations outside of the region.Tom English
September 18, 2006
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Tom: "Monte Carlo simulations use random numbers. They do not generate them. Your argument was that the only useful randomness in programs was “programmed in.” But all “programmed in” random number sequences are pseudorandom. A “truly” random sequence has to be input to the program — it is not programmed in." I didn't say that the Monte Carlo simulations produced random numbers as output; I said that they produce random numbers, which are used as input. I don't understand why you're making the distinction between "random" and "pseudo-random". Can you predict the output of a rng? If you want a "real" random number generator, then why not use a Geiger-Counter and a radioactive source, and add (integrate) the number of 'hits' over a selected time interval? T.E.: "I genuinely do not know what you are trying to say. If you agree that there were ancestors of humankind living 3.5 billion years ago, then I have, as I intended, been conservative in using the figure. That is, information has accumulated in the genome over more than 3.5 million years." I'm trying to tell you that it is easier to find a way to bacterial life than it is to eukaryotic life. Eukaryotic life appeared over a relatively short period of time. Bacteria dominated up until shortly before the pre-Cambrian. Without bothering to go look at the numbers, off the top of my head, I would say that you have, at most, 3-400 million years to basically come up with the eukaryotic genome, which has billions of bases. I say it's easier to argue to bacteria because you're probably dealing with 100's of millions of years, but the bacterial genome is of the order of 1 million bases. So with eukaryotes, you have 1000 times more work to do, in about twice the time. T.E.: "Also, if you read above, you will see that I told Gil that he really had no way to respond but to attack gradualism and invoke irreducible complexity. You have been johnny on the spot." Well, Tom, what's your proposed mechanism?PaV
September 18, 2006
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Dave, Old? I did patchboard programming in 1974-75.Tom English
September 18, 2006
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Tom English: "It is so very, very easy. First you predicate chance (sans necessity), and then you stipulate that a particular protein structure must emerge, just so, at once. But it is much harder to show that no protein structure whatsoever could ever emerge through evolution." I wouldn't quibble with what you stated. However, you are asking for a proof by negation, which is extremely hard, while at the same time ignoring that it seems as though Darwinists ought to explain how these protein molecules came about in the first place instead of asking someone to prove that every known protein molecule couldn't have emerged. You're also ignoring the fact that Fred Hoyle, Nobel Prize winner, took one look at the calculation I spoke of, and concluded that Darwinism was hokum. Accuse him of being a Creationist? Well, he was an atheist, and in lieu of Darwinism proposed panspermia. "In all data transmission, error correction reduces the probability of error, but it does not reduce it to zero. You can’t beat the Second Law. Think of it this way: What would correct an error in the error correction system? Or think of it this way: Sometimes a fruit fly has an extra leg in place of an antenna." Think of it this way: in an article in the latest issue of Nature, there is a study which identified so-called HAR genes. The authros state there that the HAR1 is a particularly highly-evolved gene in comparison with the chimpanzee genome, meaning that it has 18 mutations instead of the 1 or 2 that would be expected through random mechanisms. Would you like to explain where the extra 16 mutations came from? I'm in a rush. I'll post more later.PaV
September 18, 2006
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There is not a shred of direct evidence that any new information has entered the genome of any living thing during the course of its evolution. It may have of course but if it did where did it come from? There is also not a shred of evidence that bacteria ever evolved into anything but bacteria. The vast majority of bacteria are only varieties of a relatively few basic forms which cannot be transformed even from one to another. To be brutally honest there is no convincing evidence that any phylum ever evolved into any other phylum. They all appeared almost simultaneously including some that became extinct almost immediately. This does not mean that they were separately created however. It means only that early in the evolutionary scenario that the "prescribed" body plans were expressed very early. The history of the fossil record is the story of progressive loss of potential. The first capacity to be lost was that of producing the fundamentally different body plans that characterize the various phyla. Once produced no new ones ever appeared and some disappeared early on. Next to appear were the various classes within the phyla and once they were evident no new ones would ever appear and again some would soon disappear. Next to appear were the orders, followed by the genera and finally the species. Unlike the phyla, most have which have remained, whole orders, families, genera, and species have appeared only to become extinct. The creative capacity has steadily declined until today there is no genus that can be demonstrated to have appeared in the last two million years, during which time untold numbers of species have come and gone. I am now convinced that even no true species are being produced at present. Grasse has suggested the same as I have shown. In support of that is the failure for anyone to demonstrate creative evolution when I have offered the challenge. The present flora and fauna are the terminal products of a finished evolutionary process which will never resume. How can one further refine the structure of the elephant, the lion, the eagle or the horse? The answwer is one can't. They are the ultimate products of an orthogenetic goal-directed process which has terminated with those final immutable products. So also is Homo sapines. I repeat that we are the ultimate product of a planned and completely realized purposeful evolution in which there was never any role for chance whatsoever. Mindlessly to assume otherwise as the Darwinians insist on doing is with foundation. They apparently were simply "born that way." I am unable to offer any other explanation. The entire process was determined from begining to end and chance had no role in it. To imagine otherwise is atheist inspired mysticism and nothing more. There now, I feel somewhat better. Thanks for not listening. As near as I can tell no one ever does. For that reason alone - I love it so! "A past evolution is undeniable, a present evolution undemonstrable." John A. DavisonJohn A. Davison
September 18, 2006
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Tom Sure. The sample rate should be set by the A/D convertor. Usually that's done through an interrupt or DMA controlled by the convertor itself. That way it only records a new sample when a new sample is available. A file produced by the API should be produced in that manner. Preferably you want a 16 bit sample and take only the lowest order bit which should be noise even if it's got a live mike so long as it isn't being driven to ground or saturation. Shift the low bit of consecutive samples into a variable of the size you need and that should do it. The full size samples will have some redundancy in them as cross-talk from regular frequency sources (the switching frequency of switched power supplies for example) will show up in the sample data. That's where the "hum" comes from in old amplifiers turned up too far or those with deteriorating power supplies - the 60-hertz AC line frequency (or 50 hertz if you're across the pond) isn't adequately filtered out of the DC after rectification when electrolytic caps start drying up. It's actually 120 hertz after the rectifier. Modern power supplies are almost all switchers which operate in the high kilohertz range typically above human hearing so the hum from the old days is a relic seldom heard anymore. Now this is making ME feel like a relic from the old days. Thanks a lot. :razz:DaveScot
September 18, 2006
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Dave, Thanks. The reason I have worried about such sources of random numbers is that I know that the people measuring atmospheric noise go to some lengths to clean up the data and make it "more random." You would think data from a random noise source would not need cleaning up, but if you, say, sample at too high a rate, you can get correlated values. Again, thanks.Tom English
September 18, 2006
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Tom English I'm surprised you didn't know that a/d convertors can provide a ready source of high quality random number samples. In the immortal words of Maxwell Smart, "That's the oldest trick in the book". Here's some free source code in Visual C++ for an A/D based rng using the sound API of DirectX to get at the hardware. http://www.cyotec.com/resources/cyorand/ The following source code should show you how to get the raw sample data from a Mac to replace that from the DirectX sound API. http://developer.apple.com/samplecode/RecordAudioToFile/index.html I'm an IBM PC guru. The last Apple programming I did was almost 25 years ago on an Apple IIe.DaveScot
September 18, 2006
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Pav: "Bad calculation. The first form of life is bacterial. It shows up about 3.5 billion years ago. The conditions for life on the early earth didn’t begin until roughly that time. So I’m afraid you don’t have 3.5 billion years to work with." I genuinely do not know what you are trying to say. If you agree that there were ancestors of humankind living 3.5 billion years ago, then I have, as I intended, been conservative in using the figure. That is, information has accumulated in the genome over more than 3.5 million years. When the conditions were right for life in the oceans and in the earth is a matter of debate. "Continual increase over time is not a plausible mechanism for the accumulation of information." If you read what I wrote above, I spoke of the mean gain and the rate of gain. Neither of these implies continual gain. Also, if you read above, you will see that I told Gil that he really had no way to respond but to attack gradualism and invoke irreducible complexity. You have been johnny on the spot. So just to make everyone happy, let's emphasize that, assuming a bacterial ancestor of homo sapiens lived 3.5 billion years ago, and assuming for simplicity that the bacterium had no genetic information, evolution has gained ON AVERAGE 1.4 bits of information per year to reach the human genome.Tom English
September 18, 2006
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PaV: "It’s really quite easy to demonstrate that proteins have very little likelihood of forming by chance." It is so very, very easy. First you predicate chance (sans necessity), and then you stipulate that a particular protein structure must emerge, just so, at once. But it is much harder to show that no protein structure whatsoever could ever emerge through evolution. "Do you have some idea as to how they formed by chance, as in the first cell?" As a researcher in evolutionary computation, I have never had much reason to delve into the orgin of life. And it is funny that you should bring it up now, given that we were talking about evolution. "So there are now better generators than a Monte Carlo simulator. So what. How does that affect my argument?" Monte Carlo simulations use random numbers. They do not generate them. Your argument was that the only useful randomness in programs was "programmed in." But all "programmed in" random number sequences are pseudorandom. A "truly" random sequence has to be input to the program -- it is not programmed in. Tom: "You seem to have problems with the Second Law of Thermodynamics. That is why there must be occasional errors in reproduction." Pav: "And you seem to have problems with the repair systems that biological forms have in place. Next question please." In all data transmission, error correction reduces the probability of error, but it does not reduce it to zero. You can't beat the Second Law. Think of it this way: What would correct an error in the error correction system? Or think of it this way: Sometimes a fruit fly has an extra leg in place of an antenna.Tom English
September 18, 2006
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mike1962, Thanks for the link. I saw some time back that someone had hacked a random number generator for cryptography applications using a sound card, but I was skeptical. What you pointed me to looks good. Too bad I'm using a Mac.Tom English
September 18, 2006
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John, I couldn't possibly hold my own with you in discussion of biological evolution. You are a biologist, and I am not. But when the discussion turns to more abstract topics, I do have some things to say. "You are a hero to the 'After the Bar Closes' crowd and so apparently is Alan Fox." I've never looked at that page. The reason I'm here is that I learn a lot more engaging people with different views than I do people sharing my own view.Tom English
September 18, 2006
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kairos: "First, most of the significant advancments in the genome complexity did occur in a very narrow time range;" Evidently you have the Cambrian proliferation of body plans in mind. Due to the fact that gene expression is highly nonlinear (with genetic regulatory networks, protein interaction networks, and inter-cellular communication), small changes in genotype can account for big changes in phenotype. Provided we stick to complexity in the sense of Kolmogorov (algorithmic information, as I specified above), there's no evidence to back up your claim. "second, the more complex genomes have very limited number of organisms to decently maintain RM+NS operation;" The notion that larger populations search a fitness landscape better than smaller populations is a common misconception. Under various circumstances, a small population is more likely to escape a local maximum than is a large population. "third, and very important, arguing about the yearly rate in #bits is completely meaningless without any information about the actual regularity of the search space." Almost all fitness functions are irregular in the extreme. That is, they are algorithmically random, and thus they are easy to optimize. Let's say we uniformly draw a fitness function from the set of all functions from the space of genotypes to the set of all fitness values. Irrespective of the size of the space of genotypes, 916 fitness evaluations yield with 99.99% certainty a genotype that is more fit than 99% of the genotypes. "Regularity" of the fitness landscape says little or nothing about the difficulty of optimization. A needle-in-a-haystack function and a constant function differ very little in regularity.Tom English
September 18, 2006
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Silence is golden. It is the last refuge for the devout Darwinian. I love it so! "A past evolution is undeniable, a present evolution undemonstrable." John A. DavisonJohn A. Davison
September 18, 2006
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