Evo-Info 3: Evolution is not search

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Introduction to Evolutionary Informatics, by Robert J. Marks II, the “Charles Darwin of Intelligent Design”; William A. Dembski, the “Isaac Newton of Information Theory”; and Winston Ewert, the “Charles Ingram of Active Information.” World Scientific, 332 pages.
Classification: Engineering mathematics. Engineering analysis. (TA347)
Subjects: Evolutionary computation. Information technology–Mathematics.

Marks, Dembski, and Ewert open Chapter 3 by stating the central fallacy of evolutionary informatics: “Evolution is often modeled by as [sic] a search process.” The long and the short of it is that they do not understand the models, and consequently mistake what a modeler does for what an engineer might do when searching for a solution to a given problem. What I hope to convey in this post, primarily by means of graphics, is that fine-tuning a model of evolution, and thereby obtaining an evolutionary process in which a maximally fit individual emerges rapidly, is nothing like informing evolution to search for the best solution to a problem. We consider, specifically, a simulation model presented by Christian apologist David Glass in a paper challenging evolutionary gradualism à la Dawkins. The behavior on exhibit below is qualitatively similar to that of various biological models of evolution.

Animation 1. Parental populations in the first 2000 generations of a run of the Glass model, with parameters (mutation rate .005, population size 500) tuned to speed the first occurrence of maximum fitness (1857 generations, on average), are shown in orange. Offspring are generated in pairs by recombination and mutation of heritable traits of randomly mated parents. The fitness of an individual in the parental population is, loosely, the number of pairs of offspring it is expected to leave. In each generation, the parental population is replaced by surviving offspring. Which of the offspring die is arbitrary. When the model is modified to begin with a maximally fit population, the long-term regime of the resulting process (blue) is the same as for the original process. Rather than seek out maximum fitness, the two evolutionary processes settle into statistical equilibrium.

Figure 1. The two bar charts, orange (Glass model) and blue (modified Glass model), are the mean frequencies of fitnesses in the parental populations of the 998,000 generations following the 2,000 shown in Animation 1. The mean frequency distributions approximate the equilibrium distribution to which the evolutionary processes converge. In both cases, the mean and standard deviation of the fitnesses are 39.5 and 2.84, respectively, and the average frequency of fitness 50 is 0.0034. Maximum fitness occurs in only 1 of 295 generations, on average.

I should explain immediately that an individual organism is characterized by 50 heritable traits. For each trait, there are several variants. Some variants contribute 1 to the average number offspring pairs left by individuals possessing them, and other variants contribute 0. The expected number of offspring pairs, or fitness, for an individual in the parental population is roughly the sum of the 0-1 contributions of its 50 traits. That is, fitness ranges from 0 to 50. It is irrelevant to the model what the traits and their variants actually are. In other words, there is no target type of organism specified independently of the evolutionary process. Note the circularity in saying that evolution searches for heritable traits that contribute to the propensity to leave offspring, whatever those traits might be.

The two evolutionary processes displayed above are identical, apart from their initial populations, and are statistically equivalent over the long term. Thus a general account of what occurs in one of them must apply to both of them. Surely you are not going to tell me that a search for the “target” of maximum fitness, when placed smack dab on the target, rushes away from the target, and subsequently finds it once in a blue moon. Hopefully you will allow that the occurrence of maximum fitness in an evolutionary process is an event of interest to us, not an event that evolution seeks to produce. Again, fitness is not the purpose of evolution, but instead the propensity of a type of organism to leave offspring. So why is it that, when the population is initially full of maximally fit individuals, the population does not stay that way indefinitely? In each generation, the parental population is replaced with surviving offspring, some of which are different in type (heritable traits) from their parents. The variety in offspring is due to recombination and mutation of parental traits. Even as the failure of parents to leave perfect copies of themselves contributes to the decrease of fitness in the blue process, it contributes also to the increase of fitness in the orange process.

Both of the evolutionary processes in Animation 1 settle into statistical equilibrium. That is, the effects of factors like differential reproduction and mutation on the frequencies of fitnesses in the population gradually come into balance. As the number of generations goes to infinity, the average frequencies of fitnesses cease to change (see “Wright, Fisher, and the Weasel,” by Joe Felsenstein). More precisely, the evolutionary processes converge to an equilibrium distribution, shown in Figure 1. This does not mean that the processes enter a state in which the frequencies of fitnesses in the population stay the same from one generation to the next. The equilibrium distribution is the underlying change­less­ness in a ceaselessly changing population. It is what your eyes would make of the flicker if I were to increase the frame rate of the animation, and show you a million generations in a minute.

Animation 2. As the mutation rate increases, the equilibrium distribution shifts from right to left, which is to say that the long-term mean fitness of the parental population decreases. The variance of the fitnesses (spread of the equilibrium distribution) increases until the mean reaches an intermediate value, and then decreases. Note that the fine-tuned mutation rate .005 ≈ 10–2.3 in Figure 1.

Let’s forget about the blue process now, and consider how the orange (randomly initialized) process settles into statistical equilibrium, moving from left to right in Animation 1. The mutation rate determines

  1. the location and the spread of the equilibrium distribution, and also
  2. the speed of convergence to the equilibrium distribution.

Animation 2 makes the first point clear. In visual terms, an effect of increasing the mutation rate is to move equilibrium distribution from right to left, placing it closer to the distribution of the initial population. The second point is intuitive: the closer the equilibrium distribution is to the frequency distribution of the initial population, the faster the evolutionary process “gets there.” Not only does the evolutionary process have “less far to go” to reach equilibrium, when the mutation rate is higher, but the frequency distribution of fitnesses changes faster. Animation 3 allows you to see the differences in rate of convergence to the equilibrium distribution for evolutionary processes with different mutation rates.

Animation 3. Shown are runs of the Glass model with mutation rate we have focused upon, .005, doubled and halved. That is, uʹ = 2 ⨉ .005 = .01 for the blue process, and uʹ = 1/2 ⨉ .005 = .0025 for the orange process.

An increase in mutation rate speeds convergence to the equilibrium distribution, and reduces the mean frequency of maximum fitness.

I have selected a mutation rate that strikes an optimal balance between the time it takes for the evolutionary process to settle into equilibrium, and the time it takes for maximum fitness to occur when the process is at (or near) equilibrium. With the mutation rate set to .005, the average wait for the first occurrence of maximum fitness, in 1001 runs of the Glass model, is 1857 generations. Over the long term, maximum fitness occurs in about 1 of 295 generations. Although it’s not entirely accurate, it’s not too terribly wrong to think in terms of waiting an average of 1562 generations for the evolutionary process to reach equilibrium, and then waiting an average of 295 generations for a maximally fit individual to emerge. Increasing the mutation rate will decrease the first wait, but the decrease will be more than offset by an increase in the second wait.

Figure 2. Regarding Glass’s algorithm (“Parameter Dependence in Cumulative Selection,” Section 3) as a problem solver, the optimal mutation rate is inversely related to the squared string length (compare to his Figure 3). We focus on the case of string length (number of heritable traits) L = 50, population size N = 500, and mutation rate uʹ = .005, with scaled mutation rate uʹ L2 = 12.5 ≈ 23.64. The actual rate of mutation, commonly denoted u, is 26/27 times the rate uʹ reported by Glass. Note that each point on a curve corresponds to an evolutionary process. Setting the parameters does not inform the evolutionary search, as Marks et al. would have you believe, but instead defines an evolutionary process.

Figure 2 provides another perspective on the point at which changes in the two waiting times balance. In each curve, going from left to right, the mutation rate is increasing, the mean fitness at equilibrium is decreasing, and the speed of convergence to the equilibrium distribution is increasing. The middle curve (L = 50) in the middle pane (N = 500) corresponds to Animation 2. As we slide down the curve from the left, the equilibrium distribution in the animation moves to the left. The knee of the curve is the point where the increase in speed of convergence no longer offsets the increase in expected wait for maximum fitness to occur when the process is near equilibrium. The equilibrium distribution at that point is the one shown in Figure 1. Continuing along the curve, we now climb steeply. And it’s easy to see why, looking again at Figure 1. A small shift of the equilibrium distribution to the left, corresponding to a slight increase in mutation rate, greatly reduces the (already low) incidence of maximum fitness. This brings us to an important question, which I’m going to punt into the comments section: why would a biologist care about the expected wait for the first appearance of a type of organism that appears rarely?

You will not make sense of what you’ve seen if you cling to the misconception that evolution searches for the “target” of maximally fit organisms, and that I must have informed the search where to look. What I actually did, by fine-tuning the parameters of the Glass model, was to determine the location and the shape of the equilibrium distribution. For the mutation rate that I selected, the long-term average fitness of the population is only 79 percent of the maximum. So I did not inform the evolutionary process to seek out individuals of maximum fitness. I selected a process that settles far away from the maximum, but not too far away to suit my purpose, which is to observe maximum fitness rapidly. If my objective were to observe maximum fitness often, then I would reduce the mutation rate, and expect to wait longer for the evolutionary process to settle into equilibrium. In any case, my purpose for selecting a process is not the purpose of the process itself. All that the evolutionary process “does” is to settle into statistical equilibrium.

Sanity check of some claims in the book

Unfortunately, the most important thing to know about the Glass model is something that cannot be expressed in pictures: fitness has nothing to do with an objective specified independently of the evolutionary process. Which variants of traits contribute 1 to fitness, and which contribute 0, is irrelevant. The fact of the matter is that I ignore traits entirely in my implementation of the model, and keep track of 1s and 0s instead. Yet I have replicated Glass’s results. You cannot argue that I’ve informed the computer to search for a solution to a given problem when the solution simply does not exist within my program.

Let’s quickly test some assertions by Marks et al. (emphasis added by me) against the reality of the Glass model.

There have been numerous models proposed for Darwinian evolution. […] We show repeatedly that the proposed models all require inclusion of significant knowledge about the problem being solved. If a goal of a model is specified in advance, that’s not Darwinian evolution: it’s intelligent design. So ironically, these models of evolution purported to demonstrate Darwinian evolution necessitate an intelligent designer.

Chapter 1, “Introduction”

[T]he fundamentals of evolutionary models offered by Darwinists and those used by engineers and computer scientists are the same. There is always a teleological goal imposed by an omnipotent programmer, a fitness associated with the goal, a source of active information …, and stochastic updates.

Chapter 6, “Analysis of Some Biologically Motivated Evolutionary Models”

Evolution is often modeled by as [sic] a search process. Mutation, survival of the fittest and repopulation are the components of evolutionary search. Evolutionary search computer programs used by computer scientists for design are typically teleological — they have a goal in mind. This is a significant departure from the off-heard [sic] claim that Darwinian evolution has no goal in mind.

Chapter 3, “Design Search in Evolution and the Requirement of Intelligence”

My implementation of the Glass model tracks only fitnesses, not associated traits, so there cannot be a goal or problem specified independently of the evolutionary process.

Evolutionary models to date point strongly to the necessity of design. Indeed, all current models of evolution require information from an external designer in order to work. All current evolutionary models simply do not work without tapping into an external information source.

Preface to Introduction to Evolutionary Informatics

The sources of information in the fundamental Darwinian evolutionary model include (1) a large population of agents, (2) beneficial mutation, (3) survival of the fittest and (4) initialization.

Chapter 5, “Conservation of Information in Computer Search”

The enumerated items are attributes of an evolutionary process. Change the attributes, and you do not inform the process to search, but instead define a different process. Fitness is the probabilistic propensity of a type of organism to leave offspring, not search guidance coming from an “external information source.” The components of evolution in the Glass model are differential reproduction of individuals as a consequence of their differences in heritable traits, variety in the heritable traits of offspring resulting from recombination and mutation of parental traits, and a greater number of offspring than available resources permit to survive and reproduce. That, and nothing you will find in Introduction to Evolutionary Informatics, is a fundamental Darwinian account.

1,439 thoughts on “Evo-Info 3: Evolution is not search”

  1. keiths: Jock knows something you don’t, so your epistemic probabilities differ.

    LoL!

    Um. no. That’s not his argument. Nice of him to cover for you though. I’m beginning to think he has you on Ignore.

  2. Mung: I could say, “Yes, the probability has gone down.” And I could be honestly mistaken about that. My answer should be “I don’t know.”

    The reason the answer should be “I don’t know” is because I don’t know if any hearts remain in the deck. Putting the spade back may not change anything.

    Ack! You still really can’t handle this!
    You are talking about scenario 1:
    1) “What’s P(heart)?”
    “I don’t know”
    We remove a heart, and show (but return) a spade.
    2) “What’s P(heart)?”
    “I don’t know”
    3) “Has P(Heart) decreased since I asked you the first time?”
    “YES”
    It doesn’t matter in this scenario if there are no hearts remaining in the deck. If there were no hearts remaining, then P(Heart) has declined from 1/n to 0. That’s still a decline!
    The reason for ‘showing’ a spade in scenario 1 was to head-off-at-the-pass the special case where the deck is all hearts. “Edited to avoid weaseling”.

    Fat chance, huh.

  4. DNA_Jock: If there were no hearts remaining, then P(Heart) has declined from 1/n to 0. That’s still a decline!

    So NOW the denominator is important! So is calculation and/or estimation!

    BEFORE we drew a heart we didn’t know diddly about the probability. AFTER we drew a heart we can now assign a probability of 1/n to the event that just took place, even if we don’t know the value of n.

    And somehow, it’s not yet clear how, the probability will decrease for the next draw.

    Any minute now the light’s going to go on. 🙂

    “Has the probability decreased since I first asked you?”

    When you first asked me, the probability of drawing a heart was unknown. The probability of drawing a heart is still unknown. You’re saying it doesn’t matter if it is unknown, because it must have decreased. I have to toss out my initial “honest” answer and replace it with an estimate of 1/n even though 1/n was not the initial probability that I started out with. Have I got it?

  6. DNA_Jock,

    Mung’s claim

    Putting the spade back may not change anything.

    Jock’s proposal

    We remove a heart, and show (but return) a spade.

    Mung discusses the p(h) after the heart is removed relative to after the heart is removed. Jock discusses p(h) after the heart is removed relative to before the heart is removed. Both are right in their conclusions, however Jock created a straw-man when addressing Mung’s claim.

  7. And let me point out again that none of this involves a very large number of identical trials and the connection to Rumraket’s claims therefore remains murky at best.

  8. colewd: Mung discusses the p(h) after the heart is removed relative to after the heart is removed. Jock discusses p(h) after the heart is removed relative to before the heart is removed. Both are right in their conclusions, however Jock created a straw-man when addressing Mung’s claim.

    LOL. No, Mung created a strawman when discussing Jock’s scenario, which has always been quite unambiguous: “Has the probability decreased since I first asked you?“

  9. Mung: BEFORE we drew a heart we didn’t know diddly about the probability. AFTER we drew a heart we can now assign a probability of 1/n to the event that just took place, even if we don’t know the value of n.

    Ack! No. You are still hopelessly lost.
    Nobody “drew” a heart in scenario 1 (i.e. selected a card at random from the deck, that turned out to be a heart). I removed a heart from the deck.
    First probability is Hzero / Nzero.
    The second probability is (Hzero – 1) / (Nzero – 1), which is always smaller than Hzero/Nzero, since we know that Hzero < Nzero. Because I showed you a spade!
    FFS!

  10. So to conclude the thought in comment-184786, I revise my “I don’t know” and replace it with 1/n after seeing the heart.

    Then I see a spade. I’m too lazy to update 1/n. I put the spade back in the deck. I’m still too lazy to update 1/n. But I can reason that IF there are any hearts in the deck, n has INCREASED relative to the number of hearts in the deck. Therefore the proportion of hearts relative to n has decreased.

    But it hasn’t really decreased, because by putting the spade back in all we have done is restore the deck back to the condition it was in before we took out the spade.

    If the probability was 1/n before we took the spade out, the probability is 1/n after we put the spade back.

    So we’re back to where we were before.

    otoh. If there are now no hearts left in the deck, 0/n is less than 1/n. But I don’t know that there are no hearts left in the deck. Neither do I know how many times I should sample the deck looking for a heart before I give up.

  11. FFS Jock, the fact that you removed a spade doesn’t change the number of hearts left in the deck. And if there are hearts left in the deck you just INCREASED the probability of drawing a heart! And then by returning the spade to the deck you just restored the balance. The probability of removing a heart on the next draw, assuming there are in fact hearts left in the deck, is back to what it was before you took out the spade.

    But maybe, just maybe, by a miracle of God, you managed to remove the only heart in the deck. 🙂

    ETA: Do you have any examples that don’t involve divine intervention?

  12. DNA_Jock: Mung created a strawman when discussing Jock’s scenario, which has always been quite unambiguous: “Has the probability decreased since I first asked you?”

    The probability, when you first asked, was unknown. Another way to put it, is that it had no value. You can’t subtract from it, you can’t add to it. It’s unknown.

    In my most humble opinion, it’s not even a probability. Perhaps there is some fundamental misunderstanding on my part to understand what is and is not a probability. Maybe we should clear that up first.

    p(BEFORE DNA_Jock removed a HEART) = ????????

    Assign the value to a variable, so later we can add to it or subtract from it as required. What value do we assign to the variable?

  13. Mung: FFS Jock, the fact that you removed a spade doesn’t change the number of hearts left in the deck. And if there are hearts left in the deck you just INCREASED the probability of drawing a heart! And then by returning the spade to the deck you just restored the balance. The probability of removing a heart on the next draw, assuming there are in fact hearts left in the deck, is back to what it was before you took out the spade.

    Yes, all this is true, although the “assuming there are in fact hearts left in the deck” qualifier is unnecessary. Whatever the composition of the deck, taking any number of cards of any suit out and returning those same cards must “restore the balance”, and thus does absolutely nothing to the probability of drawing any category of card from that deck.
    True, and never been in dispute. Not what we were talking about, however.

    But maybe, just maybe, by a miracle of God, you managed to remove the only heart in the deck.
    ETA: Do you have any examples that don’t involve divine intervention?

    Well, in scenario 1, I didn’t say whether I looked at the cards before removing and burning the ten of hearts. If I did NOT look, then you got a eensy weensy bit of information about the proportion of hearts in the deck (not enough to come up with an “estimate” though). If I did look, then you are fresh out of luck there.
    That’s what I thought you were getting at when you complained that I was “cheating” by manipulating the probabilities: “Hey! You peeked at the deck! Not fair!”
    Sorry to have over-estimated you again, my bad.
    So I came up with the no-cheating, no-divine intervention, scenario 2.
    I hesitate to try to explain scenario 2 to you however. If you can’t grasp scenario 1, then scenario 2, with its two possible outcomes, will present problems.

  15. DNA_Jock: I hesitate to try to explain scenario 2 to you however. If you can’t grasp scenario 1, then scenario 2, with its two possible outcomes, will present problems.

    Don’t explain it. I was going to take it up next. I never really took it up because there’s been too many other things going on. But I shall.

  16. Scenario 2:

    Before shuffling the first time, I show you two cards, a heart and a club. After asking the first time “What’s the probability?”, I remove a card at random, show it to you, then ask the second and third questions. In this situation, neither of us knows the first or second probabilities, but we both know that the probability has changed. You know whether the probability has increased or decreased.

    1. What difference does it make whether the deck is shuffled or not?
    2. Where did the two cards you showed me come from?
    3. What’s the probability of what? Drawing a heart?
    4. The second question, just to be straight, is a repeat the first question? What’s the probability of drawing a heart?
    5. Third question is, just to be clear, “Has the probability that the next draw is a heart decreased?”

    Are these the questions:

    First question: What’s the probability of drawing a heart from this deck?
    Second question: What’s the probability that you draw a heart from this deck?
    Third quesiton: Has the probability of drawing a heart decreased since I first asked you?

    Final question (for now). Given the way you worded your questions, why were you so astonished that I should speak of “drawing a card” rather than “removing a card”?

  17. Here’s one definition of probability:

    probability – the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.

    So if the ratio of the favorable cases to the whole number of cases is unknown do we even have a probability?

  18. Another definition of probability:

    a number that represents how likely it is that a particular thing will happen

    What is the numerical value of “I don’t know”? Is it “I don’t know” or some other numerical value?

    ETA: If we don’t have a numerical value, do we have a probability?

  19. Mung,

    Is it finally dawning on you why I used the phrase “epistemic probability”?

  20. Mung:
    Here’s one definition of probability:

    probability – the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.

    So if the ratio of the favorable cases to the whole number of cases is unknown do we even have a probability?

    Only a relative probability, not an absolute probability. And I think this is important, because much of our lives we spend playing what we know are relative probabilities. We can know that the probability of an accident is higher if we drive drunk, even if we can’t know the absolute probability of an accident either drunk or sober. We are constantly trying to improve our chances, no matter that they can never be precisely calculated in most cases.

  21. keiths: Is it finally dawning on you why I used the phrase “epistemic probability”?

    Not really. What’s a probability that is not “epistemic” look like?

  22. Coming from the guy who’s been trying to dismiss epistemic probability as “made up”, that’s pretty amusing.

  23. keiths: Coming from the guy who’s been trying to dismiss epistemic probability as “made up”, that’s pretty amusing.

    Finally something we can agree on. Now was that really so hard?

  24. DNA_Jock: First probability is Hzero / Nzero.
    The second probability is (Hzero – 1) / (Nzero – 1), which is always smaller than Hzero/Nzero, since we know that Hzero < Nzero. Because I showed you a spade!
    FFS!

    Could you explain this? Hzero is zero hearts? Does zero mean ‘0’, as in 1 – 1 = zero = 0? What does ‘zero’ stand for?

  25. Mung: Could you explain this? Hzero is zero hearts? Does zero mean ‘0’, as in1 – 1 = zero = 0? What does ‘zero’ stand for?

    Hzero = initial number of hearts
    Nzero = initial number of cards

  26. ^^^ What dazz said.
    Sorry, I couldn’t be faffed to do proper subscripts.
    OTOH I don’t think that that would have made any difference.

  29. Jock:

    ^^^ What dazz said.
    Sorry, I couldn’t be faffed to do proper subscripts.
    OTOH I don’t think that that would have made any difference.

    I’m not even sure that dazz’s explanation will penetrate.

  30. keiths:
    Mung,

    Is it finally dawning on you why I used the phrase “epistemic probability”?

    Let me guess, Is it because you were searching for” eczema problem “and it popped up?

  31. All,

    The only way to learn the stuff you’re talking about is to do a lot of work with it — usually beginning with exercises that are graduated in difficulty. Those of us who have worked with it a lot make the mistake of thinking that we can get others to understand by explaining it well. Our un-exercised minds would not have grasped the explanations that our exercised minds think are clear and simple.

    I’ll hazard a guess that Mung reads the books he owns, and gets the feeling that he understands what he’s reading, but doesn’t work the problems. I hasten to add that I’ve done the same. In fact, I understand these (white-bearded-and-balding) days that it was the fundamental cause of some errors that I published.

    What’s going on here is not what brought this to mind (see “Evo-Info 1: Engineering Analysis Construed as Metaphysics“). But reflecting on it has brought some clarity. Marks, Dembski, and Ewert are producing in faithful readers the feeling that they understand the math, when they don’t understand it at all. Their trick is to express the math in terms of high-school concepts, and suggest that its easy to understand. Then readers who don’t understand tell themselves that they must understand because, hey, it’s only high-school math. I don’t want to counter by producing in readers the feeling that they understand my explanation of what the math of MDE actually says. Then it comes down to: whom are you going to believe, a man in league with the Great Deceiver, or your wise and Christian guides to knowledge of the Truth? And, in any case, the proper response to indoctrination is not counter-indoctrination, but instead education.

    But I’m not going to get people to learn math in a setting like this. People have to work with it to grasp it. So what am I trying to achieve? (You might want to ask yourselves the same question. It’s fine by me if you can show that it’s the wrong question to ask. But “Mung is dumb, and it benefits the world to put Mung’s dumbness on exhibit” won’t cut the mustard.)

  32. Tom is right. And I am perfectly capable of putting my own dumbness on exhibit, thank you very much. I don’t need anyone’s help.

  35. phoodoo: If math doesn’t equate to reality, why must one bother to understand the math?

    What does “equate to reality” have to do with anything?

    We study and use mathematics, because it is useful. Whether or not it equates to reality is beside the point.

  37. Mung:
    Why the hell is this thread still featured? It died and it’s stinking up the front page.

    Must be still searching out a mechanism for eukaryogenesis, including searching the missing genes, that is not gradual and yet fits into Darwinian narrative…whatever that is… 😉

  38. Every time I crack open a book on evolution it presents evolution as a problem solver., a designer, an engineer, a search.

  39. Mung:
    Every time I crack open a book on evolution it presents evolution as a problem solver., a designer, an engineer, a search.

    You forgot evolution as miracle performer as Harshman already agreed it is…
    miraculously inserting genes into the supposed tree of life…

  45. Joe Felsenstein: Take that, Isaac Newton, you and your fancy equations!

    Let’s work out some Joe Felsenstein’s equations!

    According to him we have 10 billions species on earth all of them evolving and in transition into other species…

    So if that is true, there should be trillions of transitional fossils everywhere…

    Not only that, I should have thousands, if not tens of thousands of transitional fossils under the grass just in my backyard…

    Let populations genetics do the math and let us see the truth!

  48. J-Mac: Einstein was wrong more than once…So I guess that doesn’t make him a god…

    With respect to the orbit of Mercury he was right at least once. Do you think being right about something makes you a God?

  49. newton: With respect to the orbit of Mercury he was right at least once. Do you think being right about something makes you a God?

    Some thought for the longest time that Einstein was never going to be proven wrong…therefore considered him a god…

    He was proven wrong about entangled particles “communicating” faster than the speed of light, cosmological constant, time in relation to theory of relativity at least in some aspects…etc…though he did say more than once time was an illusion…I have to agree… 😉

  50. J-Mac: Let’s work out some Joe Felsenstein’s equations!

    According to him we have 10 billions species on earth all of them evolving and in transition into other species…

    So if that is true, there should be trillions of transitional fossils everywhere…

    Not only that, I should have thousands, if not tens of thousands of transitional fossils under the grass just in my backyard…

    How the hell do you conclude from the above that there should be tons of fossils everywhere?

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