Wednesday, March 24, 2010

Evolution: A One-in-a-Billion Shot

It is no surprise that there are scientific problems with evolution. Its predictions are continually turning out to be false. It undoubtedly ranks number one in faulty expectations. For instance, one of its primary predictions, common descent, has badly failed. The reconciliation of the molecular and the visible, morphological, features has been a major problem in trying to resolve the evolutionary tree. The molecular and morphological features often indicate "strikingly different" evolutionary trees that cannot be explained as due to different methods being used.

The growing gap between molecular analyses and the fossil record, concluded one researcher, "is astounding." Instead of a single evolutionary tree emerging from the data, there is a wealth of competing evolutionary trees. And often what evolutionists conclude is downright strange. Over time insects must have evolved wings, then lost them in the evolutionary process only then later yet again to evolve them (or less parsimoniously, the wings could have disappeared over and over throughout the tree). Or again, bats must have independently evolved, in separate lineages, the same intricate echolocation capability.

As one researcher put it, "Phylogenetic incongruities can be seen everywhere in the universal tree, from its root to the major branchings within and among the various taxa to the makeup of the primary groupings themselves." These are not minor statistical variations and the general failure to converge on a single topology has some researchers calling for a relaxation from "tree-thinking."

And this is but a sampling of the many falsified predictions of evolution. There are many more where these came from as evolutionists are constantly surprised. You can see 14 basic predictions that were falsified here. Predictions which evolutionists are absolutely sure of are routinely found to be false. "I about fell off my chair" is the typical refrain of evolutionists.

Obviously the scientific evidence does not bode well for evolution. One way to evaluate the theory is with Bayes' theorem which states that for any given scientific observation, O, the probability a theory, T, is true, given that observation, is the probability of the theory prior to the observation multiplied by the probability of the observation given that the theory is true, divided by the probability of the observation without knowing whether the theory is true or not. It sounds complicated but the formula is simple:

P(TO) = P(T) * P(OT) / P(O)

Bayes' theorem gives us a way to evaluate a theory given a series of observations. A difficulty, however, is that the probabilities are difficult to gauge. What is P(T), P(OT) and P(O)? What we can do is use a conservative computation, giving evolution favorable treatment at every turn.

Consider the ratio P(OT) / P(O). If an evolutionist is certain that observation, O, will not be observed, then the numerator should be quite low, say one in a million or one in a thousand. If P(O) is 0.5 then the ratio would be 0.000002 or 0.002, respectively. But to be conservative, and give evolution favorable treatment, let's set the ratio to 0.2, orders of magnitude greater than is reflected in the evolutionists expectations.

For our 14 falsified predictions, using these extremely conservative values, Bayes' theorem tells us that evolution is a one-in-a-billion shot. This calculation is conservative, and there are many more falsified predictions for which to account. But you can see the religion behind evolution did not lead to a very good scientific theory.

48 comments:

  1. Nice article. Evolutionists pay only lip service to falsifiability. Their motto seems to be, "deny any falsification". By the way, The first link in the third paragraph seems to be broken:

    http://www.blogger.com/www.pnas.org/content/95/12/6854.full

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  2. How many times has Bayes' theorem proven false?

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  3. I appreciate the article. As a pastor and apologist, this blog has been an excellent resource for me.
    Respectfully,
    Pastor Adam Barton, Akron, OH

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  4. When trying to reconstruct the history of millions of years old events, expect surprises.

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  5. And when basing that history on imagination surprises come with the package anywho...

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  6. When trying to reconstruct the history of millions of years old events, expect surprises.

    And when jumping out of a window sometimes expect to be "surprised" to fly up because gravity does not apply? Remember that charlatans have been saying that the forces guiding "evolution," whatever it is, are as well understood as gravity.

    The truth is that imagining things about the past may have little to do with biology, which should largely be the study of life here and now. Why do we need to play pretend that we have certain knowledge of what happened millions of years ago? Currently millions upon millions of embryos unfold (the original meaning of evolve) into the same general forms and types while organisms select a mate based on knowledge of their species, specification and form and so on and on and on. This process can be observed and experienced here and now. Yet supposedly imaginary evidence in an imaginary past shows that the knowledge and sentience which we experience (and can rationally infer that other organisms experience also) is an illusion that reduces to blind and ignorant processes or mechanisms.

    At least proponents of ignorant views of that sort unwittingly seek to reduce their intellects to blind and ignorant processes, thus explaining their own ignorance and stupidity.

    It's ironic that biologists often claim a knowledge of all life and its significance in the entire Cosmos (not to mention multiple and of course imaginary universes as well) based on brains that they think* reduce entirely to unthinking, unknowing processes.

    *Of course whatever they supposedly think or know is just a metaphor that actually reduces to ignorance based on things like natural selection operating on the reproductive organs of a group of ancient ape-like creatures and so on.

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  7. Dr. Hunter writes:
    Predictions which evolutionists are absolutely sure of are routinely found to be false.

    Yet, as we are continually reminded, one of the hallmarks of science is that science makes predictions, whereas ID does not.

    Does evolutionary science have special immunity from falsified predictions? Have evolutionary scientists allotted themselves a quota of falsified predictions, but they have not yet reached that quota?

    The fundamental problem with predictions is that a verified prediction does not entail that the hypothesis on which the prediction is based is true.

    The success of a prediction would seem to depend on how well the phenomenon under investigation is understood to begin with. A misunderstood phenomenon would lead to a misinformed prediction. And a misinformed prediction could lead to an erroneous conclusion, either a false positive or a false negative, which may or may not be perceived by the investigator.

    How often does science encounter a situation like Einstein's visualization of a light beam emanating from one side of an accelerating elevator and striking the opposite wall at a lower position, and his concluding that the force of gravity could bend light?

    Science cannot discount the value of making and verifying predictions, but if science continues to ignore falsified predictions, what does that say about science?

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  8. mynym: Remember that charlatans have been saying that the forces guiding "evolution," whatever it is, are as well understood as gravity.

    The usual statement is that evolution is as much a fact as gravity. The mechanisms are constantly being investigated, and the history, like all histories, is revised when new information becomes available.

    mynym: Why do we need to play pretend that we have certain knowledge of what happened millions of years ago?

    Let's start with something simple: Dinosaurs once roamed the Earth. Can we be fairly certain of this claim? Or are all historical claims scientifically unsupportable?

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  9. And when basing that history on imagination surprises come with the package...

    Ironically given an unfalsifiable paradigm of progress any surprises within it can be cited as evidence that the overall mythology is correct. After all, it supposedly shows progress in knowledge. It's a fairly seamless and simple mythology in which the main tenet is a vague notion of evolutionary progress, not any specific/falsifiable scientific theory.

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  10. Doublee: Does evolutionary science have special immunity from falsified predictions?

    Nope. That's why today's Theory of Evolution is not your parent's Theory. The Theory has been repeated modified since Darwin first introduced it. However, the fundamental claims are still intact, including Common Descent across most taxa, descent with modification, and natural selection as an important mechanism of adaptation.

    Doublee: The fundamental problem with predictions is that a verified prediction does not entail that the hypothesis on which the prediction is based is true.

    That's correct. However, when we have verified predictions by independent observers, independent methodologies, and even different fields of sicence, then we gain confidence in the scientific validity of the claim. The Theory of Evolution predicts molecular data and geological data, which can be verified by different scientists using completely different methodologies approaching the problems from completely different directions.

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  11. The nested hierarchy, as it applies to most traits and organisms, is an *observation*. From this strongly supported observation, we can make a number of verifiable predictions. However, there is ambiguity at the trunk of the tree of life, as well as ambiguity in cases of rapid radiations. Of the former, the data supports horizontal evolution rather than vertical descent. Of the latter, it can be difficult to resolve divergences that happened in geologically short periods of time, but the node still fits within the larger phylogenetic tree. Though this may be contrary to a simplistic view of evolution, it doesn't mean that evolution hasn't occurred.

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  12. The usual statement is that evolution is as much a fact as gravity.

    Which is false because there is no specified theory of evolution. Even proponents like Gould are still seeking to define its structure and after 1,343 pages there is generally only Darwin, natural selection and the tree of life. Natural selection tends to falsify theories of progressive evolution while the tree of life is often falsified. So to the extent that evolution, whatever it is, has been specified it has been falsified. (And it generally has not been specified, certainly not to the same extent that the theory of gravity is.)

    Or are all historical claims scientifically unsupportable?

    Historical claims should generally be supported with actual evidence, not imaginary evidence. It's a relatively simple distinction that most evolutionists seem to have a hard time with.

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  13. Zachriel: The usual statement is that evolution is as much a fact as gravity.

    mynym: Which is false because there is no specified theory of evolution.

    A fact is not a theory. The Theory of Gravity is currently in a state of flux with several competing theories.

    mynym: Even proponents like Gould are still seeking to define its structure ...

    Gould has been dead for quite a few years. Glad he's still seeking.

    mynym: Natural selection tends to falsify theories of progressive evolution while the tree of life is often falsified.

    The nested hierarchy is still intact for the vast majority of taxa. And where it doesn't apply, new and testable evolutionary theories have been proposed. Ironically, many of them were linked in the original post.

    Zachriel: Or are all historical claims scientifically unsupportable?

    mynym: Historical claims should generally be supported with actual evidence, not imaginary evidence.

    So the answer is "yes," we can make scientifically supportable historical claims, including "knowledge of what happened millions of years ago." It does require evidence, of course.

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  14. However, the fundamental claims are still intact, including Common Descent across most taxa....

    These are the most specific, defined or fundamental claims. Which is ironic as even they are similar to the hypothetical goo that Darwin sought to reform into an actual scientific theory. Even a central pillar like common descent is not as defined as it appears to be given that many biologists have said that abiogenesis is a non-issue to them. Given that it's not clear just how common, common descent is supposed to be. There could be a singular origin of life, a few or even more than a few. Many creationists would agree that a few original kinds of life gave rise to life as we know it.

    ...descent with modification...

    I agree that change happens, much like excrement.

    ...and natural selection as an important mechanism of adaptation.

    If anything natural selection tends to undermine progressive creation myths or progressive hypotheses of evolution.

    It can be observed in action yet we can also observe that its predictions are also falsified in many cases (to the extent that they were specified in the first place). This makes it clear that it is not central to evolution or change as we know it.

    The theory of evolution at its most defined (nested hierarchy/common descent and natural selection) is actually not that defined and to the extent that it is specified it has often been falsified. Much more so than the theory of gravity. And this is focusing on where some are attempting to rigorously specify an actual "theory of evolution" out of the hypothetical goo typical to the progressive creation myths that have always been with us. There is still an "overwhelming" amount of imaginary evidence mistaken as evidence of some sort when it comes to evolution in general.

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  15. And where it doesn't apply, new and testable evolutionary theories have been proposed.

    Of course, what wouldn't be an evolutionary theory? One in which change did not exist or some such? At any rate, there is a difference between having a theory open to verification and falsification and having numerous hypotheses.

    So the answer is "yes," we can make scientifically supportable historical claims, including "knowledge of what happened millions of years ago." It does require evidence, of course.

    Of course you can make claims but they're not all epistemic equals as per the argument of propagandists who insist that "evolution" based purely on bind and ignorant processes is as much a fact as is gravity or the fact that the earth is round and so on.

    So the answer is "yes," we can make scientifically supportable historical claims, including "knowledge of what happened millions of years ago." It does require evidence, of course.

    As I pointed out in this thread on the rare occasions when imaginary evidence of the sort you cite has been subject to falsification, it has been falsified. So perhaps what is currently being imagined about the skeletal remains of organisms would be falsified in that case as well. In any event, that's apparently some of the best evidence you have for your purported knowledge of what happened millions of years ago yet it is certainly not the epistemic equivalent of facts supporting the theory of gravity. If the skeletal remains of that fish were not found would that have been counted as a falsification of the so-called "theory of evolution"? Not if history is any measure, yet supposedly a highly specified "scientific theory" has been verified when they are found. If evolution is a scientific theory, using the term science loosely, it certainly is not the equivalent of all others.

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  16. The relevant comments with respect to imagining things about the skeletal remains of organisms begin here

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  17. Zachriel:
    "The nested hierarchy, as it applies to most traits and organisms, is an *observation*."

    And we shouldn't observe it with descent with modification.

    Nested hierarchies require progress and descent with modification does not.

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  18. mynym: Of course, what wouldn't be an evolutionary theory?

    One without descent with modification.

    mynym: At any rate, there is a difference between having a theory open to verification and falsification and having numerous hypotheses.

    Yes, and the Theory of Evolution makes many falsifiable claims, including about mechanisms and their relationships and histories.

    mynym: If the skeletal remains of that fish were not found would that have been counted as a falsification of the so-called "theory of evolution"?

    New organisms are discovered every day, extant and extinct. Each is a potential falsification of one aspect of the Theory of Evolution or the entire theory.

    Start with something simple, Common Descent in land vertebrates. We not only have the fossil succession; fishopods to amphibians to reptiles to mammals to primates to humans; but we also have the nested hierarchy. If we take the various traits of land vertebrates, and arrange them parsimoniousy, do they form a reasonably consistent nested hierarchy?

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  19. Zachriel:
    "Common Descent in land vertebrates. We not only have the fossil succession; fishopods to amphibians to reptiles to mammals to primates to humans; but we also have the nested hierarchy."

    And that nested hierarchy 1) is not based on descent with modification and more importantly 2) is not expected from descent with modification.

    As for "fossil succession", well we have fossils anyway...

    What we don't have is any genetic data which would demonstrate that the transformations required are even possible.

    No way to test it- no way to measure it- no way to study it- no way it belongs in a science classroom.

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  20. Earlier Zachriel linked to Tiktaalik.

    However there is evidence that tetrapods already existed by the time Tiktaalik shows up.

    And that means Tiktaalik is nothing more than a mosaic- something we should expect to find in that type of environment.

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  21. One without descent with modification.

    History shows that any theory of change which can be portrayed as progressive will be called evolution no matter how you are specifying it now, even with being as vague as you are. If variation arose spontaneously without any link to descent then that would be called evolution and seamlessly woven into progressive creation myths. Ironically things would have been much simpler and intuitive for proponents of progressive creation myths if Lamarckism instead of Mendelism had be verified, "evolution" would have been just as true in the minds of biologists. As it always must be. Similarly if a tree of life is observed then it is evolution, yet if no tree of life is observed then we are assured that "evolution," whatever it is, is still true.

    Yes, and the Theory of Evolution makes many falsifiable claims, including about mechanisms and their relationships and histories.

    There is no theory of "evolution," although you seem to like to play pretend. Even the theory of natural selection is difficult to derive falsifiable claims from. After all, it apparently explains altruism and selfishness equally well. Given that Darwin made theological arguments and the tradition continues, here is an interesting question: How would you create life to falsify progressive creation stories or "evolution" and provide evidence that life was created? Is this even possible? Darwinists seem to say that it is often enough in the abstract (things should look one way if created, not another), so what should the structure of life be if a singular Creator did create it?

    Each is a potential falsification of one aspect of the Theory of Evolution or the entire theory.

    What sort of organism could be discovered which would falsify the entire theory? And on the other hand, what sort of structure should life have if it was designed based on knowledge (as opposed to a metaphorical Blind Watchmaker) with purposes in mind? Darwinists have made all sorts of philosophical and theological arguments about design, so one is left wondering exactly what sort of observations they have in mind. For instance, apparently if babies were born without birth defects and if we didn't have back pain then they would all be theists or treat it as scientific evidence that a Creator existed? If the heavens weren't so large and were laid out in perfect geometrical shapes with the earth in the center then they would supposedly treat that as scientific evidence for a Creator? I doubt it. After all, they've already said a priori that they must always seek explanations that seem natural to them, whatever natural means. And apparently it means anything and everything but a Designer. It's interesting that many act as if some observation or another is evidence that falsifies the notion of a Designer when they've already maintained that there is no evidence which would verify it.

    What sort of structure should life have if it was designed? How would you design it? No nested hierarchy? Why?

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  23. OK Lee-

    Please show us where in the theory of evolution that a griffin would falsify the theory.

    Or perhaps you could provide some reasoning.

    The same for a centaur and a precam rabbit.

    BTW there isn't any guarantee that any bacteria will survive if a population is exposed to anti-biotics.

    As for the bald proclamation by the NAS- hilarious.

    How can it be a unifying concept when its grandest claims can't even be tested?

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  24. Apparently the theological and philosophical arguments Darwinists often make are not coherent logically. No one here seems willing to try to support them with logic.

    Please show us where in the theory of evolution that a griffin would falsify the theory.

    It seems to me that a platypus fits the bill of a mosaic as much as an imaginary organism like the griffin would. What can be observed in reality already challenges and defies the imagination to the point that some apparently become confused and mistake their imaginations for reality merely because they can imagine things. It's often that difficult. At any rate, it doesn't really matter given that evolution hasn't been specified to predict one sort of organism or another in the first place. If griffins were observed then I would imagine that they would make perfect sense in light of evolution, just like everything else does.

    On the other hand, if I was a singular Creator leaving evidence of that fact in biology one of the best ways probably would be mosaics of some sort. One would need to falsify nature based commonality or phylogeny yet still show a common source for the way things unfold/evolve.

    Or perhaps you could provide some reasoning.

    Apparently he's already retracted whatever he was imagining. It really shouldn't be that hard to come up with numerous falsifications for a rigorously specified scientific theory like "evolution." After all, as Zach has noted it is just like the theory of gravity.

    A possible explanation for theological arguments of this sort may be historical. Note that the story of a provincial Christian who goes on a journey and finds answers to his religion in the Darwinian creation myth is so common that it is provincial itself. The mythology of Progress that typifies his new creation myth just happens to match his own supposed progress from ignorance to knowledge. The irony is that he typically becomes an imbecile easily overwhelmed by illusions of knowledge based on little more than imagining things about the past due to the structure of Darwinian "reasoning." Even blogs written by people of this sort are named after theological arguments like the “panda’s thumb,” which has more to do with their own sectarian religious past and/or the historical roots of Darwinism than science. The theological and philosophical arguments typical to Darwinists seem to be rather puerile and shallow, something along the lines of: “God wouldn’t make a panda’s thumb like this because a perfect God wouldn't tinker.” And so on. Perhaps that’s because they typically leave their original faith as an ignorant schoolboy. At any rate, religious arguments about what God would or would not do have absolutely nothing to do with what natural selection actually does and there is little evidence that it "creates" thumbs.

    The same for a centaur...

    Ironically the urge to merge illustrated in ancient nature based paganism doesn't seem all the different from the Darwinian urge to merge based on naturalism.

    At any rate, I can imagine that a centaur would be incorporated in evolutionary creation myths easily enough. Why don't proponents of ID work their way around to citing their own imaginations as the equivalent of scientific evidence or a scientific theory? If they ever have they certainly haven't done so to the same extent that Darwinists have. It often seems that the real issue is different psychological patterns seen politically in the general patterns of left/imagery/blurring/tolerance and right/iconoclasm/discrimination.

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  25. Dear Mr Hunter,

    I do not think your calculations make any sense.

    First of all, to compute the undonditional probability P(O), you need the conditional probabilities. Let’s say there are two theories, D(esign) and E(volution). Bayes’ formula states

    P(E|O)=P(O|E)P(E)/P(O)

    where

    P(O)=P(O|E)P(E)+P(O|D)P(D)

    The only probability we could even hypotheically hope to estimate is P(O|E). When you assume that P(O) is 1/2 and that P(O|E) is “small,” you are imposing conditions on the remaining probabilities.

    Second, the probabilities are not “difficult” to gauge, they are impossible to gauge. What is P(D)? Some would say 0, some would say 1. Let’s not even get into the philosophical issues of assigning probabilities to events that have already happened.

    Third, the values used are not “extremely conservative,” they are completely arbitrary.

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  26. peter olofsson:

    ====
    I do not think your calculations make any sense.

    First of all, to compute the undonditional probability P(O), you need the conditional probabilities.
    ====

    What's wrong with using a large value?


    ====
    Third, the values used are not “extremely conservative,” they are completely arbitrary.
    ====

    Do false predictions count?

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  27. If P(O|E) is small and P(O) is 1/2, P(O|D) cannot also be small. Thus, you sneak in an assumption about the likelihood of the observation under a design hypothesis. But your evolutionist would not make that assumption. Indeed, if he thinks P(O|E) is small, then P(O) will also be small and the ratio close to 1.

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  28. peter olofsson:

    Sorry, I meant the prior, P(E), not P(O). Sorry for the confusion.

    I assume you don't have a problem with starting with a conservatively high value for P(E).

    Next we have P(O). I agree it cannot be computed. I thought I made it clear that I am using a conservative bound for the ratio P(O|E) / P(O), rather than using the total probability theorem to get at P(O).

    You suggest the ratio is close to unity for small P(O). When evolutionists make high-confidence predictions which they are quite certain of, that means that the actual observation, O, which falsified the prediction, reduces the probability of evolution. This is true regardless of P(O). The ratio P(O|E) / P(O) is always going to be small for observations that falsify high-confidence predictions. The value of 0.2 is incredibly conservative and evolution-friendly calculation.

    That is why I ask: Do false predictions count? If one cannot accept even such a conservative calculation, then it appears false predictions do not and we're dealing with theory protectionism. Protectionism is the strategy evolutionists often use.

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  29. peter olofsson:

    Following up. Consider the possibility that the ratio P(O|E) / P(O) is close to unity, as you suggest. IOW, the P(O|E) values are say 10^-6, but P(O), as it turns out, always just happens to be very small and not much larger than 10^-6, so the ratio is always almost 1.0.

    In that case, the probability of evolution, given all those falsified predictions, remains pretty high. The price we pay for this is that evolution becomes unfalsifiable, as Popper suggested. IOW, the falsification of all these fundamental predictions has essentially no effect on its probability.

    And of course there is no justification for making all the P(O) values so small. I've done several other calculations, such as uniformly randomizing P(O). You always obtain small probabilities for evolution.

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  30. Cornelius,

    Thanks for the clarification, I should have understood you meant P(E).

    Whether you use the total probability theorem or not, it is there. Bounds on the ratio P(O|E)/P(O) cannot be chosen independently of the probabilities involved. Let's try some numbers. We want P(E) to be large, let say 0.999. Then we want P(O|E) to be small, let's say 0.01. What is P(O)? Well, it depends on what other hypotheses there are. Let's say there's only one, D, which then has P(D)=0.001. The total probability theorem gives

    P(O)=P(O|E)P(E)+P(O|D)P(D)=0.00999+P(O|D)*0.001

    which means that the ratio P(O|E)/P(O) equals

    0.01/(0.00999+P(O|D)*0.001)

    The smallest possible value of this ratio is obtained if P(O|D)=1 and equals 0.91. Thus, your "incredibly conservative" value of 0.2 cannot even be obtained.

    Different values of P(E) and P(O|E) give different lower bounds of course, but for your calculations you would need an upper bound and that would depend on P(O|D). I doubt your evolutionist would give it a very high value.

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  31. Cornelius,
    I agree, we could set P(E)=1 and make evolution a priori true (or set P(E)=0 and make it a priori false). One could always argue what the probability P(E) really means, and that's why I also think it's meaningless to talk about "conservative" numbers; there is simply no benchmark with which to compare. It one in a million a small probability? Not compared to one in a billion which in turn is huge compared to one in a trillion, and so on.

    However, if one attempts to use Bayes' theorem, everything comes down to the numbers one chooses, and you cannot avoid invoking alternative hypotheses and the probabilities of observations under these hypotheses.

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  32. Cornelius,
    You say that you have "done several other calculations, such as uniformly randomizing P(O)." If you have them posted somewhere, please let me know. I am curious as to how you are doing it.

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  33. peter olofsson:

    ==========
    Whether you use the total probability theorem or not, it is there. Bounds on the ratio P(O|E)/P(O) cannot be chosen independently of the probabilities involved. Let's try some numbers. We want P(E) to be large, let say 0.999. Then we want P(O|E) to be small, let's say 0.01. What is P(O)? Well, it depends on what other hypotheses there are. Let's say there's only one, D, which then has P(D)=0.001. The total probability theorem gives

    P(O)=P(O|E)P(E)+P(O|D)P(D)=0.00999+P(O|D)*0.001

    which means that the ratio P(O|E)/P(O) equals

    0.01/(0.00999+P(O|D)*0.001)

    The smallest possible value of this ratio is obtained if P(O|D)=1 and equals 0.91. Thus, your "incredibly conservative" value of 0.2 cannot even be obtained.

    Different values of P(E) and P(O|E) give different lower bounds of course, but for your calculations you would need an upper bound and that would depend on P(O|D). I doubt your evolutionist would give it a very high value.
    ==========

    You doubt an evolutionist would give P(O|D) a very high value in this scenario of two, mutually exclusive, theories that provide completeness? It sounds like he is having it both ways. The observation, O, is unlikely on evolution and on design? That doesn't make much sense. In fact, if he says O is unlikely on evolution, then it is *likely* on design. P(O|D) is the complement of P(O|E) :

    P(D) = 1 - P(E)
    P(O|D) = 1 - P(O|E)

    so,

    P(O) = P(O|E)P(E) + P(O|D)P(D)
    P(O) = P(O|E)P(E) + [1-P(O|E)]P(D)
    P(O) = P(O|E)P(E) + [1-P(O|E)] [1 - P(E)]

    so,

    P(E|O) = [P(O|E) / P(O)] P(E)
    P(E|O) = [ P(O|E) / [ P(O|E)P(E) + [1-P(O|E)] [1 - P(E)] ] ] P(E)

    P(E|O) = 1 / [ 1 + [1-P(O|E)] [1 - P(E)] / [P(O|E)P(E)] ]


    Using your numbers P(E|O) comes out to 10^-23 for the fourteen observations, far worse than my conservative calculation of 1 in a billion.

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  34. Cornelius,
    Speaking of having it both ways, I can's comment on your stats, but the methodology you're employing here seems remarkably similar to that employed by SOber in the PNAS paper you are always touting. THere, he uses the two competing hypotheses of separate and common descent and says that as separate descent becomes less likely, common descent becomes more likely. you claim that this shows evolution is a metaphysical theory because some hypotheses of separate descent (such as those espoused by Answers in Genesis) are based on religious tenets. Yet here you are comparing evolution and design, when some hypotheses of design (for example Dembski's ideas) are based on religious tenets . is your methodology now metaphysical as well? you can't have it both ways.

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  35. Dear Cornelius,

    1. You are wrong about basic probability again:

    P(O|D) DOES NOT EQUAL 1-P(O|E)!

    There is no such rule for conditional probabilities, Additivity applies to the event left of the conditioning bar, not the one to the right.

    2. I find it interesting that you insist on your bound being "conservative" despite the fact that I demonstrated it being mathematically impossible. I showed that P(T|O) is at least 0.91, yet you claim it is less than 0.2. Explanation?

    3. To get a conservative bound, you must assign a value to P(O|D). Since you are the one claiming this type of analysis is meaningful and detrimental to evolution, what value do you choose and why?

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  36. Correction to (2) above: I showed that the ratio
    P(O|E)/P(O) is at least 0.91, yet you claim it is less than 0.2.

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  37. peter olofsson:

    =====
    1. You are wrong about basic probability again:

    P(O|D) DOES NOT EQUAL 1-P(O|E)!

    There is no such rule for conditional probabilities, Additivity applies to the event left of the conditioning bar, not the one to the right.
    =====

    Of course, that was a model for use in your scenario. You suggested that the evolutionist, in addition to predicting that P(O|E) is low, would also want P(O|D) to be low. That conveniently protects evolution from falsifying observations, but doesn't seem realistic. For these types of predictions, these conditional probabilities are more likely to be opposed.

    So if this isn't fair, let's use something more conservative. How about P(O|D) = (1-P(O|E)) / 10. Surely that is a conservative model. So with P(O|E) set to 0.01, then P(O|D) is about 0.1. Pretty small. Good enough? In that case the 14 observations results in P(E|O) of 10^-10.


    ========
    2. I find it interesting that you insist on your bound being "conservative" despite the fact that I demonstrated it being mathematically impossible. I showed that P(T|O) is at least 0.91, yet you claim it is less than 0.2. Explanation?
    ========

    If you use the total probability theorem, as I showed above, then P(E|O) is 0.91 for a single observation. But additional observations drive it down further.

    =====
    3. To get a conservative bound, you must assign a value to P(O|D). Since you are the one claiming this type of analysis is meaningful and detrimental to evolution, what value do you choose and why?
    =====

    I discussed P(O|D) in #1 above. We agree that the choices for these probabilities are difficult to defend. But I think multiple false predictions should count somehow, and I'm trying to show this using conservative assumptions. Even then it can be challenged, I agree, but then we're headed toward unfalsifiability. For instance, one could say P(O|D) is always really small, as you have suggested. But this seems like special pleading. At some point E becomes unfalsifiable if we just arbitrarily reduce P(O|D) to save it.

    ReplyDelete
  38. 1. What constitues a "conservative" bound is in this context completely arbitrary. Why is P(O|D)=0.1? Why not 0.001 or 0.00000000000001 or something else? What is D anyway? The only conditional probability you can even hypothetically hope to estimate is P(O|E) since E(volution) is defined via mutation and selection which is a stochastic process, allowing for probability calculations, at least in theory. Practically, it's very difficult though, depending on what O is. To get to P(O|D) you need to specify what D is and what probability it confers on O, not just arbitrarily claim that a value of 0.1 is "good enough."


    2. It is AT LEAST 0.91. You cannot achieve anything with LOWER bounds, you need upper bounds. Interestingly, you still do not seem to acknowledge that your "conservative" value of 0.2 is mathematically impossible.

    3. I agree, multiple false predictions should count somehow. I just don't see much promise in using Bayes' theorem (even applied correctly). The conclusions depend so heavily on arbitrary probaility assignments that they become meaningless. The opposite of arbitrarily reducing P(O|D) is arbitrarily inflating it and there is no objective way to assert either.

    By the way, thanks for letting me discuss these issues at your blog!

    ReplyDelete
  39. Clarification of (2) above: You claimed that P(O|E)/P(O) is at most 0.2; I proved that it is at least 0.91.

    ReplyDelete
  40. peter olofsson:


    ============
    2. It is AT LEAST 0.91. You cannot achieve anything with LOWER bounds, you need upper bounds. Interestingly, you still do not seem to acknowledge that your "conservative" value of 0.2 is mathematically impossible.
    ============

    No, 0.2 is not mathematically impossible. It is conservative given the high confidence of the evolutionary predictions. How does that work in your example? Yes, the ratio is "AT LEAST 0.91" when P(D) has that small value. But in your scenario, it grows as P(E) reduces, because they are complementary. So the ratio reduces well below 0.2.


    ============
    By the way, thanks for letting me discuss these issues at your blog!
    ============

    Absolutely, you are always welcome.

    ReplyDelete
  41. Cornelius,

    (1) If a number is at least 0.91, it is mathematically impossble that it is less than 0.2. I stand dogmatically by this statement until you prove me wrong. :)

    (2) Now, you are the one who suggested a "very high" value of P(E) and a "quite low" value of P(O|E). I chose 0.999 and 0.01 for the sake of argument (you suggested P(O|E)=0.1 but nothing for P(E); I assume "very high" is more extreme than "quite low"). If you don't like my choice of numbers, provide your own. Please suggest a "very high" value of P(E), a "quite low" value of P(O|E) that gives a ratio
    P(O|E)/P(O) that is "well below 0.2."

    (3) Again, my bound is a LOWER bound so it is useless to your type of conclusion.

    ReplyDelete
  42. peter olofsson:

    ==========
    (1) If a number is at least 0.91, it is mathematically impossble that it is less than 0.2. I stand dogmatically by this statement until you prove me wrong. :)
    ==========

    That seems strange. After an observation, P(E) is reduced, so P(D) increases. After several observations the ratio reduces below 0.2. For example, the dominant terms become:

    P(E|O) = [ P(O|E) / P(O|D) / [1 - P(E)] ] * P(E)

    so the ratio might be:

    P(O|E) / P(O|D) / [1 - P(E)]

    = 0.01 / 0.1 / 0.9 = 0.11 < 0.2

    Much lower values are possible with easily feasible, higher values of P(O|D) and lower values of P(O|E).

    ReplyDelete
  43. We're talking about the ratio P(O|E)/P(O) per your original post, nothing else. This is the quantity I showed to be at least 0.91, with my proposed probabilities. Now you are computing something else. Let's stay focused.

    ReplyDelete
  44. peter olofsson.

    ====
    We're talking about the ratio P(O|E)/P(O) per your original post, nothing else. This is the quantity I showed to be at least 0.91, with my proposed probabilities. Now you are computing something else. Let's stay focused.
    ====

    Of course, with your proposed probabilities, P(O|E)/P(O) is at least 0.91.

    ReplyDelete
  45. Very good, always nice to agree on something. Anyway, I think your main problem is not so much in the math as in the philosophy; how can one reasonably assign probabilities such as P(O|D) which are, invariably, needed for any upper bounds.

    ReplyDelete
  46. peter olofsson:

    Yes, I agree that a Bayesian approach can't get you very far in problems like these. But false predictions ought to count (as I know you agree). I take a different approach here:

    www.DarwinsPredictions.com

    where I evaluate the reaction of evolutionary theory to the falsified expectations. Obviously there are times when a falsified prediction does a theory little harm, but other times when there really is a fundamental problem. This becomes rather obvious in the adjustments the theory must make in reaction to the observation.

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  47. nano:

    =====
    Speaking of having it both ways, I can's comment on your stats, but the methodology you're employing here seems remarkably similar to that employed by SOber in the PNAS paper you are always touting. THere, he uses the two competing hypotheses of separate and common descent and says that as separate descent becomes less likely, common descent becomes more likely. you claim that this shows evolution is a metaphysical theory because some hypotheses of separate descent (such as those espoused by Answers in Genesis) are based on religious tenets.
    =====

    The arguments for evolution are *explicitly* metaphysical and religious. This isn't a "claim" I'm making. You are promoting a religious theory that is contradicted by the science.


    ====
    Yet here you are comparing evolution and design, when some hypotheses of design (for example Dembski's ideas) are based on religious tenets . is your methodology now metaphysical as well? you can't have it both ways.
    ====

    That was peter o's scenario that I was responding to. And more importantly, the calculation was driven by scientific problems with evolution.

    ReplyDelete
  48. I agree with Cornelius insofar as this particular discussion was about probability calculations pertaining to scientific inference, not about metaphysics. I enjoyed the exchange, perhaps there will be a continuation in the future. Thanks for the link. Cheers!

    ReplyDelete