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# Evolution And Probabilities: A Response to Jason Rosenhouse

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I recently published an article on Uncommon Descent on the value of probabilistic arguments in the evolution debate. Mathematician and ScienceBlogs contributor Jason Rosenhouse has since responded with a rebuttal on his blog. Here, I offer a brief response.

Rosenhouse writes,

Jonathan M. is completely confused about what the issue is. Pigliucci certainly never claimed that biologists are not interested in evaluating probabilistic feasibility (whatever that even means). He said simply that evolutionary biologists do not assign probabilities to specific events in the way that ID folks would like.

For example, Jonathan M. points to a calculation in which biologist Sean Carroll estimated the probability of obtaining the same mutation four times independently in different orders of birds. In such a narrowly defined situation the problem has more to do with combinatorics than probability, and we can be confident that all of the relevant variables can be approximated with reasonable accuracy.

He also points to a paper by Durrett and Schmidt, in which they evaluated the probability of obtaining two particular mutations in at least one individual of a population. Once again, in such a narrowly defined situation it is possible to get a grip on all of the relevant variables. But notice that neither they, nor Carroll, were trying to calculate the probability of evolving a flagellum or anything remotely like that.

While it is true that the individuals in question do not attempt to calculate the probability of something of the complexity of a bacterial flagellum, to handwavingly assert that such calculations have no bearing whatsoever on questions such as this seems to me to be somewhat naive.

For example, let’s grant for purposes of our argument here that the conclusions reached in Douglas Axe’s bacterial population model are correct: That is, if a duplicated gene is neutral, then the maximum number of mutations that a novel innovation in a bacterial population can require is up to six, whereas if the duplicated gene has a slightly negative fitness cost, the maximum number drops to two or fewer. If one can demonstrate that the evolutionary steps to a functioning flagellum would likely require more co-ordinated mutations than this at the individual stages, then — even though the exact probability of the flagellum may not be directly calculable — it seems to be a plausible inference that the flagellum lies beyond the reach of the Darwinian mechanism.

But here’s the thing. According to Douglas Axe’s more recent research, done in collaboration with Ann Gauger, even a seemingly trivial switch from Kbl to BioF function requires at least seven co-ordinated mutations, putting the transition well beyond the reach of a Darwinian process within the time allowed by the age of the earth. Their paper studies the PLP-dependent transferases superfamily. They identified a pair within the superfamily with close structural similarity but no overlapping function. The enzymes chosen were Kbl (which is involved in threonine metabolism) and BioF (which is part of the biotin synthesis pathway). And they used a three-stage process (which you can read about here) to identify which sequences were most likely to confer a change in function.

And thus they estimated that seven or more mutations would be required to convert Kbl to BioF function.

Axe and Gauger’s paper is not an isolated result. For example, one fairly recent review in Nature reported that changing an enzyme’s chemistry may require multiple neutral or deleterious mutations.

When these results are taken into account in the context of the predictions of population genetics with regards the waiting time for multiple co-ordinated non-adaptive mutations which are required to facilitate a given transition, the situation for neo-Darwinism appears to be bleak.

In the case of the Durrett and Schmidt (2008) paper, evolutionary biologist Richard von Sternberg has applied the equations employed in that paper to whale evolution. The evolution of Dorudon and Basilosaurus (38 mya) may be compressed into a period of less than 15 million years. Such a transition is a fete of genetic rewiring and it is astonishing that it is presumed to have occurred by Darwinian processes in such a short span of time. This problem is accentuated when one considers that the majority of anatomical novelties unique to aquatic cetaceans (Pelagiceti) appeared during just a few million years – probably within 1-3 million years. The equations of population genetics predict that – assuming an effective population size of 100,000 individuals per generation, and a generation turnover time of 5 years –  according to Richard Sternberg’s calculations and based on equations of population genetics applied in the Durrett and Schmidt paper, that one may reasonably expect two specific co-ordinated mutations to achieve fixation in the timeframe of around 43.3 million years. When one considers the magnitude of the engineering fete, such a scenario is found to be devoid of credibility. Whales require an intra-abdominal counter current heat exchange system (the testis are inside the body right next to the muscles that generate heat during swimming), they need to possess a ball vertebra because the tail has to move up and down instead of side-to-side, they require a re-organisation of kidney tissue to facilitate the intake of salt water, they require a re-orientation of the fetus for giving birth under water, they require a modification of the mammary glands for the nursing of young under water, the forelimbs have to be transformed into flippers, the hindlimbs need to be substantially reduced, they require a special lung surfactant (the lung has to re-expand very rapidly upon coming up to the surface), etc etc.

Moreover, Michael Behe has shown (see chapter seven of The Edge of Evolution) that the evolution of protein-protein binding sites by Darwinian means is immensely improbable. And Douglas Axe, Robert Sauer, Sean Taylor and others have shown that the preponderance of evolutionarily relevant (i.e. functional) protein folds is astronomically rare within sequence space. These types of problems are only accentuated a thousand fold when one considers systems which, by their very nature, require multiple inter-dependent protein interactions in order to perform their functions.

Jason Rosenhouse also mentions the well-known Wilf and Ewens PNAS paper:

This paper by Wilf and Ewens, also mentioned in the post, puts some mathematical meat on the bones of Dawkins’ suggestion. They are working with probabilities only indirectly, and certainly were not trying to assign precise numerical values to specific evolutionary events.

The abstract of this paper reported,

Objections to Darwinian evolution are often based on the time required to carry out the necessary mutations. Seemingly, exponential numbers of mutations are needed. We show that such estimates ignore the effects of natural selection, and that the numbers of necessary mutations are thereby reduced to about K log L, rather than KL, where L is the length of the genomic “word,” and K is the number of possible “letters” that can occupy any position in the word. The required theory makes contact with the theory of radix-exchange sorting in theoretical computer science, and the asymptotic analysis of certain sums that occur there.

This sounds awfully like an attempt to demonstrate the probabilistic plausibility of Darwinism to me. We ID proponents employ probabilistic logic as well, in order to ascertain the likelihood of evolutionarily relevant innovations emerging by Darwinian means. Only we reach the opposite conclusions from those reached by Wilf and Ewens. Darwinists are happy for probabilistic reasoning to be employed only when it suits their purposes in vindicating Darwinism. When ID proponents want to use probabilistic arguments to falsify Darwinism, they won’t be having any of it.

Douglas Axe humorously noted at the time,

If you search the current issues of professional science journals, I doubt you’ll find any papers titled “The Moon Orbits the Earth” or “Copper Conducts Electricity.” Assertions like these would work as section headings in an elementary science textbook, but no scientist would consider them newsworthy, for the simple reason that they aren’t.

Things are different in evolutionary biology, though. Here is a field that somehow never outgrew the need to reiterate its most basic tenets, as though its practitioners never had enough confidence in them to let them stand on their own two feet.

Lee Spetner points out the crippling problems with the paper:

Their model does not mimic natural selection at all. In one generation, according to the model, some number of potentially adaptive mutations may occur, each most likely in a different individual. W&E postulate that these mutations remain in the population and are not changed. Contrary to their intention, this event is not yet evolution, because the mutations have occurred only in single individuals and have not become characteristic of the population. Moreover, W&E have ignored the important fact that a single mutation, even if it has a large selection coefficient, has a high probability of disappearing through random effects [Fisher 1958]. They allow further mutations only in those loci that have not mutated into the “superior” form. It is not clear if they intended that mutations be forbidden in those mutated loci only in those individuals that have the mutation or in other individuals as well. They have ignored the fact that evolution does not occur until an adaptive mutation has taken over the population and thereby becomes a characteristic of the population. Their letter-guessing game is more a parody of the evolutionary process than a model of it. They have not achieved their second goal either.

If Darwinism can’t even handle the trivial, then what chance does it have when it comes to the bigger problems such as building flagella? And if we can’t even evaluate the probabilistic feasibility of the Darwinian mechanism, how can we ever learn whether it is up to the task at hand? Whether they realize it or not, Pigliucci and his ilk have, in effect, rendered Darwinism unfalsifiable.

"Math simply helps creationism(s) because of the great odds evolutions demands as a constant operation." Well actually, math helps the intelligent design hypothesis, but I don't see how it would ever help something so identity-of-the-intelligent designer oriented like creationism. Just saying ;)LivingstoneMorford
August 25, 2011
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Math in biology is only relevant upon a presumption that biological change happened and happens on happanchance. Otherwise math folks got nothing to say about evolution if they put their mind to math stuff. I was banned on Jason Rosenhouse blog etc for no good reason except difference of opinion and found him unreasonable generally. Anyways biology don't need help from geology or math to makes its cases. Math simply helps creationism(s) because of the great odds evolutions demands as a constant operation.Robert Byers
August 25, 2011
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And BTW by turning A-L into one genera you should be able to see what a mess of a "tree" you are going to have if you tried to include all organisms.Joseph
August 24, 2011
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1- You wouldn't know it's genealogical arrangement. It is possible to have grandchildren without any of your DNA. Also nesting is not subordinate. Nesting is groups within groups- that is what a nested hierarchy is -> groups WITHIN groups. That said a family "tree" doesn't even form a tree and that is decent with modification at the lowest level (sexually reproducing organisms)- no nested hierarchy in a family tree. 2- If they blend together at the fork there isn't anything that keeps them blended all the way through.Joseph
August 24, 2011
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At least we've peeled back a few layers to get to the underlying foundation of unshakable faith. It's refreshing.ScottAndrews
August 24, 2011
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Elizabeth: Since joining the blogosphere in 2004, I have consistently said that if Darwin has entitled his book, Origin of Adaptations I wouldn't have any problems with it. Or, as a contemporary critic of Darwin said: "As to what is old in the theory, the theory is correct; as to what is new in the theory, it is wrong." Any half-witted soul can figure out that biological forms are plastic; that's what breeders do.PaV
August 24, 2011
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There were two questions I posed. The first had to do with specified complexity in general. The second had to do with specified complexity as it applies to biology.PaV
August 24, 2011
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Does the Grand Canyon represent some specified pattern, known beforehand? Does biology?wd400
August 24, 2011
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Have you even read these passages in context? Here's was comes before the first quote
Nevertheless, their genealogical arrangement remains strictly true, not only at the present time, but at each successive period of descent. All the modified descendants from A will have inherited something in common from their common parent, as will all the descendants from I; so will it be with each subordinate branch of descendants at each successive stage.
i.e. there is a true pattern of descent(with nested 'subordinate' branches). But if some descendends are radically changed it's difficult for us to place them in that true pattern even though "their genealogical arrangement remains strictly true" As for the second one, here's what follows:
We shall see this by turning to the diagram [A tree!]: the letters, A to L, may represent eleven Silurian genera, some of which have produced large groups of modified descendants, with every link in each branch and sub-branch still alive; and the links not greater than those between existing varieties. In this case it would be quite impossible to give definitions by which the several members of the several groups could be distinguished from their more immediate parents and descendants. Yet the arrangement in the diagram [a tree remember] would still hold good and would be natural; for, on the principle of inheritance, all the forms descended, for instance from A, would have something in common. In a tree we can distinguish this or that branch, though at the actual fork the two unite and blend together
wd400
August 24, 2011
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could throw Darwinian theory into doubt.
Indeed. But that's because it's almost certainly correct.Elizabeth Liddle
August 24, 2011
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Elizabeth, It's not remotely credible that any new evidence of any kind could throw Darwinian theory into doubt. The use of probability or empirical evidence to determine what may or may not happened has already been tossed to the wind. Suppose you find a frog with opposing thumbs that flies like bat and spins webs. What are you going to say - its evolution would be improbable? Is it more improbable than the exact shape of the Grand Canyon? You have forfeited the use of probability to determine which events are more or less likely to have occurred. When you speak of probability, it is abstract, meaningless. Or will you say that Darwinian evolution is not the best explanation? That's hasn't stopped anyone yet. When Dawkins wants to wow us with real-life observations of evolution in progress he uses the changing sizes of lizard heads. And from that you extrapolate spiderwebs and echolocation, etc. etc., etc. The Discovery Channel will tell our children, 'Isn't it amazing that this thumb-using, web-weaving, flying frog evolved!' All connection to reality has been replaced with buzzwords and hand-waving. It's been said so many times that it sounds real. It's not credible that any new evidence could shatter such faith.ScottAndrews
August 24, 2011
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Not "explained away", ScottAndrews. Bat wings aren't homologous with bird wings or insect wings - they are different "solutions" to the "problem" of how to make a wing.Elizabeth Liddle
August 24, 2011
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Joseph,
Behaviour trumps genetics when it comes to adaptation. That is it is easy to change one’s behaviour in response to a changing enivironment.
Just wonder how long it would take me to change my behavior to a diet of eucalyptus leaves like the koala did.Cabal
August 24, 2011
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"I think you’ll have to give a specific example. I thought you were talking about ERVs." My argument works for both ERV phylogenies and other molecular phylogenies. But I'll stick with ERV phylogenies: Consider that both chimpanzees and humans share a number of chromosomes located in the same position in their genomes -- implying common ancestry. The odds of this occurring by chance is next to nil, BUT we could argue: you don't know what environments chimps and humans have been in, in the past, so you can't say that it must be the result of common ancestry. It could actually be that those ERVs were inserted independently in each lineage and then kept in each lineage because they offered a selective advantage. You can't argue against that, 'cause after all we don't know the environments that both species were in, right?LivingstoneMorford
August 24, 2011
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If, however, we suppose any descendant of A or of I to have become so much modified as to have lost all traces of its parentage in this case, its place in the natural system will be lost, as seems to have occurred with some few existing organisms.-Charles Darwin chapter 14
That means the tree will be artificial.
Extinction has only defined the groups: it has by no means made them; for if every form which has ever lived on this earth were suddenly to reappear, though it would be quite impossible to give definitions by which each group could be distinguished, still a natural classification, or at least a natural arrangement, would be possible.- Charles Darwin chapter 14
The tree requires those (impossible) definitions to determine the population's place on it. No definitions, no tree.Joseph
August 24, 2011
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EDTA:
It seems that to discuss speciation, one would have to have a solid definition of “species”. Is the concept more clear than the Wikipedia article (on “species”) makes it sound when it says, “Over two dozen distinct definitions of ‘species’ are in use amongst biologists.”?
Interestingly, no. The concept of speciation is completely unambiguous, at least for sexually reproducing populations. That doesn't mean that it isn't a process that takes place over times, and remains somewhat reversible for quite a while, making the point at which you declare that it has finished i.e. where you declare you have two separate species, somewhat arbitrary. But that doesn't make the concept ambiguous at all, any more than the concept of development is ambiguous, even though it is hard to say precisely when a child becomes an adult, as reflected in the term "adolescence". Perhaps we should talk about speciolescence.Elizabeth Liddle
August 24, 2011
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Yes, I know. But typically I hear the amazing adaptive powers of RM+NS described as more than a hunch. If you're still speculating about the mechanics then apparently you haven't come across anything that's convinced you much.ScottAndrews
August 24, 2011
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The first quote doesn't say there will be a tree. That is because it will be difficult to place them in one. That means it isn't a naturally created tree. The seciond quote demolishes the tree and says some other arrangement should still be possible. Also YECs accept speciation, even though it is an ambiguous concept. And the ToE does not forbid convergence on diverged lines- meaning it does not predict a tree.Joseph
August 24, 2011
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Joseph, I too have become disillusioned by Darwin's thoughts. His mistake was to extrapolate too widely what he observed to be a variation within a species. It just does not work that way! But as of the 19th century that was really a good try. In defence of Darwin personally, I can say that he was really careful in his scientific investigations, wrote wonderfully and phrased his hypotheses very accurately (which unfortunately cannot be said about many of his followers). His "On Origin of Species" is an interesting reading. But, alas, that was a big mistake to generalise his findings too widely.Eugene S
August 24, 2011
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Elizabeth, For some curious reason I can't put a comment under your comment #2.1.1.1.2. Anyway, what do you think is better: to come up with an estimate which maybe crude or to say we can't say anything? You willl agree with me if I say that In general when doing research you come up with something that fits your data and revise it, if necessary, as soon as more data becomes available. If you have no data, you may resort to "common sense" and come up with some "zero-knowledge default" model that you can work with, again until such times as (more) data is available. In fact, I read an article by Douglas Axe where he proposed a conservative estimate and he explained why it was conservative. He deliberates at length in response to criticisms at his Biological Institute's website. IMHO, this is far better that to say we can't establish an estimate. Because if we can't, why bother?Eugene S
August 24, 2011
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"There is always room for hunches. It goes like this: hunch-speculation-theory-hypothesis-prediction-test. Rinse and repeat." Agreed, actually; but it ain't over with "test," it's then onto more and more questions with the results of tests before you can actually arrive at conclusions. And if you start with the wrong hunches (assumptions) you may end up with incorrect interpretations of results. That's why you must try to rule out other possibilities; which is not what Darwinists have done. What they've done is to implement their little tests (GAs for example) and then run with the results saying: "see, this proves evolution," without actually asking any further questions: Are my hunches (assumptions correct)? Is random mutation and natural selection the only possibility, or could something else be going on? e&.... In other words, it's very easy to "prove" what you've already assumed by your hunch. Did it ever occur to you that the most reasonable assumption would be based on the issue of probabilities? Let's take clairvoyance for example: James Randi is offering \$1,000,000 to anyone who can demonstrate clairvoyance. Why is he being so bold? It all has to do with probabilities. It is highly improbable that clairvoyance is genuine. Now let's assume that you applied your hunch-followed by theory/hypothesis/test method to clairvoyance. Well, ok, you assume at the beginning that there ARE instances of genuine clairvoyance. So you theorize. Then you hypothesize that a 33% success rate in a controlled setting would be evidence of clairvoyance, since it's above the 25% threshold of chance with such "predictions." You predict (since you already believe that clairvoyance is genuine) that you will get the desired results. And lo and behold, in one instance of amazing accuracy, you arrive at 32%; a little less than you predicted, but you're ok with it. You publish your results in a peer reviewed parapsychology journal and voila. It becomes fact. Actually, according to Wiki, such a test was done: "One controlled procedure has invited 'senders' to telepathically transmit one of four visual images to 'receivers' deprived of sensation in a nearby chamber (Bem & Honorton, 1994). The result? A reported 32 percent accurate response rate, surpassing the chance rate of 25 percent." http://en.wikipedia.org/wiki/Clairvoyance If your hunch tells you that something's wrong here, you're right. Continuing....."But follow-up studies have (depending on who was summarizing the results) failed to replicate the phenomenon or produced mixed results (Bem & others, 2001; Milton & Wiseman, 2002; Storm, 2000, 2003)." Question: If Darwinian evolution depends on similar but much lower probabilities than clairvoyance, why don't your "hunch meters" turn on? They ought to have some sort of automatic switch that goes on when you're faced with near impossible odds, don't you think? And if for scientifically minded people, the issue of clairvoyance rests in the probabilities, why doesn't the issue of RM + NS also rest in the probabilities; which are next to zilch? The "clairvoyants" actually have one up on you. At least they've been bold enough to attempt to demonstrate it. Where's the claimed instance of RM + NS producing novel features under controlled tests? Well it ain't happening because it can't be. It's an issue of long periods of time for which anybody's guess is accepted provided they can make it stick with "scientificiness" (that's scientific sounding truthiness. I suppose you're going to say "well, Darwinian RM + NS has been involved in more than just one particular study; so the analogy is bogus." Well, no. Throwing 3,000,000 arrows towards a target and missing gets you the same results as throwing just one arrow towards a target and missing. You'd think by now those odds would mean something to you.CannuckianYankee
August 24, 2011
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The first quote says life is a tree, but sometimes creatures evolve is such a way it's difficult for humans to place them in that tree (cf Placazoa) The second one seems to be saying specifically that there is a tree - that there is a natural pattern which could be used to group species even if we had all the transitional forms which would do away with traditional taxonomic distinctions. But you don't have to go to The Origin to know what evolution predicts - speciation is a very basic part of evolutionary biology. Speciation makes lineages which go off to explore (and change) the fitness landscape on their own which is why, say, bats and birds have such different wings to do the same job.wd400
August 24, 2011
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There is always room for hunches. It goes like this: hunch-speculation-theory-hypothesis-prediction-test. Rinse and repeat.Elizabeth Liddle
August 24, 2011
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Forget the turtles. It's hunches all the way down . . .Eric Anderson
August 23, 2011
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Speciation isn’t an ambiguous concept though. It’s pretty clear.
It seems that to discuss speciation, one would have to have a solid definition of "species". Is the concept more clear than the Wikipedia article (on "species") makes it sound when it says, "Over two dozen distinct definitions of 'species' are in use amongst biologists."?EDTA
August 23, 2011
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I thought this whole thing was at least half-baked. How is there room left for hunches to explain how it works?ScottAndrews
August 23, 2011
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H;mm: Ever heard of the statistical weight of a macrostate? (Aka, thermodynamic probability.) When states come in identifiable clumps, the relative sizes of the clumps can be important. The key idea of FSCI is that the functional state we may observe comes from a relatively narrow and unrepresentative zone of possibilities, as opposed to the overwhelming number of unspecified gibberish states. When that happens, an unintelligent sampling of the space is overwhelmingly likely to land in typical -- gibberish -- states. BTW, this is very close to the reasoning behind the 2nd law of thermodynamics, as has been repeatedly pointed out. Under the relevant likely forces at work, a canyon of large size was an overwhelmingly probable outcome, and the particular outcome comes from an overwhelming cluster of possibilities. If on the other hand we had seen smooth-sided canal like features, similar to the Panama canal or the one at the Isthmus of Corinth, that would have been a giveaway that this was an artifact. See how the explanatory filter could have been applied? Now, let us get back to the main issue from this red herring. GEM of TKIkairosfocus
August 23, 2011
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Related:
Irreducible Complexity in Mathematics, Physics and Biology Uncommon Descent, January 31, 2007, posted by scordova The cause of incompleteness Uncommon Descent, November 3, 2009, posted by niwrad
rhampton7
August 23, 2011
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By that argument absolutely anything is possible. A monkey can type Shakespeare because the exact configuration of blades of grass on the earth is highly improbable, and yet there it is. I can throw a lump of dirt at a wall, and the exact configuration of sand and rocks will be highly improbable. So is it reasonable to expect that it might turn into a life form? After all, both are improbable. Tonight I'm going to teach my five year old how to see through that reasoning.ScottAndrews
August 23, 2011
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Elizabeth Liddle:
The first quote doesn’t seem to say what you are saying.
Correct but it supports the claim we shouldn't expect a tree.
The second quote seems to say the opposite of what you are saying: “still a natural classification, or at least a natural arrangement, would be possible.”
As in some arrangement other than a tree.Joseph
August 23, 2011
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