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. DNA_Jock: Already answered, Mung. In the comment that you were replying to, even.

    I disagree. Your comment only told us what we don’t need to know, not what we do need to know.

    One does not need to know the absolute probability of an event, or even have a way of calculating it, in order to be able to describe situations in which the probability has increased or decreased.

    ok. So what do we need to know?

  2. DNA_Jock: That’s quite the admission.

    Are you paying attention?

    Rumraket: I guess one can be forgiven for misreading my original statement that way, but now that clarification has been offered multiple times, and I have explicitly denied advancing a line of reasoning like the one you try to connect me with, shouldn’t you stop trying to connect me with it?

    Mung: My recent post has nothing to do with independent events. It has to do with sampling. It has to do with not specifying either the number of eyes sampled nor the number of “not eyes” sampled. It has to do with not knowing what the relative frequencies are because we lack the relevant data.

  3. Mung: DNA_Jock: Already answered, Mung. In the comment that you were replying to, even.

    I disagree. Your comment only told us what we don’t need to know, not what we do need to know.

    One does not need to know the absolute probability of an event, or even have a way of calculating it, in order to be able to describe situations in which the probability has increased or decreased.

    ok. So what do we need to know?

    ROFL, Mung. Not in the excerpt of the comment that you chose to quote, in the rest of the comment. Y’know, the bit you skipped.
    Sad.

  4. keiths: You are still utterly baffled by the concept of epistemic probability.

    And absolute probability. I am confused about that too! I’m confused about all sorts of made up things

    Why don’t you just cut to the chase and share with us your full knowledge about eyes and eye evolution and the associated probabilities? Epistemically speaking, of course.

    #BoyGenius

  5. DNA_Jock: ROFL, Mung. Not in the excerpt of the comment that you chose to quote, in the rest of the comment. Y’know, the bit you skipped.

    This?

    …if we gather additional data, wherein the numerator increases by a greater factor than the (vaguely defined) denominator could possibly increase, then our best estimate of the quotient will be revised upwards.

    So give me an example. Balls from bags and then eyes. Try not to cover ground that’s already been covered. Such as declaring that we pull out more red balls than green balls.

    ETA: So if the number of eyes that we observe increases the estimate of the quotient will be revised upwards. Relative to what? Seriously, I get the distinct sense you don’t read what I write.

  7. DNA_Jock: See post 596

    Did you know that comments are actually numbered such that if you want to identify a specific comment you can actually do that by referring to that specific number? And you can do it without needing to use a formula or taking people off ignore. For example, your comment, which I quoted, is comment 184479.

    Imagine that! What will they think up next DNA_Jock?

    KISS

  8. Hey phoodoo, I see that my previous estimate was wrong and that I need to adjust it. My previous estimate was either high, or low, or the same. I really don’t know. I failed to make a meaningful estimation in the first place. I’m not sure it matters.

    I think I’ll raise it, just for the hell of it. Because I usually underestimate things. I think I’ll raise it by 10 percent. Because why not!

  9. Allan Miller: But when you don’t even know the proportions, pulling a second gives you extra information about what’s in the bag – you are getting closer to discovering the unknown actual frequencies, refining your initial assessment if based only upon the first.

    But that extra information has to be relative to some other information in order for it to be useful in discovering the unknown actual frequencies and to help you refine your initial assessment. Oh, and you need an initial assessment in the first place.

    What’s your initial assessment wrt the distribution of eyes?

    ETA: see also

  10. DNA_Jock: Rumraket’s point, AIUI, was that if our sampling reveals multiple separate occasions where event X occurred, then our best estimate of how unlikely event X is gets revised.

    Does it get revised up? Or down? And what was our best estimate? Perhaps our best estimate was over-optimistic and we keep having to revise it downward.

    In that case, what then does our pulling out an eye tell us?

  11. DNA_Jock: Cute, though, that you have invoked an entirely different fallacy, the Gambler’s Fallacy, and gotten Mung’s mischaracterization of Rumraket’s point BACKWARDS:

    So you were fully aware that I wasn’t accusing Rumraket of the Gamblers Fallacy. Glad we settled that.

  12. DNA_Jock: I made no argument whatsoever about the absolute probability of evolving an eye.

    As near as I can tell you’ve made no argument about the relative probability of evolving an eye either. What figures are you using for the probabilities associated with eyes?

  13. Mung:

    What was the probability it had only green balls before we started? No one knows. So did the probability increase or decrease? Obviously, this is all quite far over my head.

    keiths:

    Obviously. You are still utterly baffled by the concept of epistemic probability.

    Mung:

    And absolute probability. I am confused about that too! I’m confused about all sorts of made up things

    Why make that dumb statement when you could simply Google “epistemic probability” instead?

    You’re a mess, Mung.

  14. keiths: Why make that dumb statement when you could simply Google “epistemic probability” instead?

    I could Google “absolute probability” too. But what would that get me other than a list of links?

    ETA: Absolute probability judgement is a technique used in the field of human reliability assessment (HRA), for the purposes of evaluating the probability of a human error occurring throughout the completion of a specific task.

    Oh yeah. That helped. Alot.

  15. keiths: You’re a mess, Mung.

    Meanwhile, you keep trying to change the subject. Anything to change the subject.

    Your probability calculations wrt the eye. You have them or you don’t. Go ahead, make some up if you need to. 🙂

  16. DNA_Jock: ROFL, Mung. Not in the excerpt of the comment that you chose to quote, in the rest of the comment. Y’know, the bit you skipped.
    Sad.

    Been there. Mung’s pathetic trademark

  17. Mung: Did you know that comments are actually numbered such that if you want to identify a specific comment you can actually do that by referring to that specific number? And you can do it without needing to use a formula or taking people off ignore. For example, your comment, which I quoted, is comment 184479.

    Yes, yes I did. I have even used “links” to allow readers to easily access the original comment.
    Whatever will they think of next. Kisses to you too.

    Mung: Does it get revised up? Or down? And what was our best estimate? Perhaps our best estimate was over-optimistic and we keep having to revise it downward.

    By George, she’s got it!
    By George, she’s got it!

    Mung: So you were fully aware that I wasn’t accusing Rumraket of the Gamblers Fallacy. Glad we settled that.

    No, you naughty boy. You accused Rumraket of the reverse Gambler’s fallacy (i.e. hot streaks exist), but then, sharing a giggle with phoodoo, invoked the straight Gambler’s Fallacy (we’re ‘due’ for a reversal), which phoodoo later ascribed to me, Rumraket, whomever. And you admitted as much. You deserve each other.
    🙂

    Mung: As near as I can tell you’ve made no argument about the relative probability of evolving an eye either.

    That’s right! I have restricted myself to explaining how you mischaracterized Rumraket’s point. You seem rather slow on the uptake.

  18. DNA_Jock: That’s right! I have restricted myself to explaining how you mischaracterized Rumraket’s point.

    Rumraket’s point, if he can be said to have one, is that 1) Eyes are not improbable and 2) it is easy to evolve an eye.

    Those are the two claims that were made that he chose to defend.

    Neither claim has been supported by anything even remotely resembling evidence or had any actual calculated probabilities associated with them. And you haven’t tried either. Nor has keiths.

    You have been missing the point all along.

    If you actually have a probabilistic argument with regard to eyes I sure would love to hear it. What’s your best guess as to how improbable they are?

  19. keiths:

    Why make that dumb statement when you could simply Google “epistemic probability” instead?

    Mung:

    I could Google “absolute probability” too. But what would that get me other than a list of links?

    ETA: Absolute probability judgement is a technique used in the field of human reliability assessment (HRA), for the purposes of evaluating the probability of a human error occurring throughout the completion of a specific task.

    Oh yeah. That helped. Alot.

    That’s pitiful, Mung. I advise you to google “epistemic probability”, so you google something else and then complain about the results.

  20. Person of Normal Intelligence:

    Bung, why are you standing in the middle of the freeway? You’re going to get yourself killed!

    Bung:

    You have no idea whether I’m in any danger. Present your calculations.

    PoNI:

    Are you crazy? You don’t need a calculated number to know that you’re in danger.

    Bung:

    Your claim hasn’t been supported by anything even remotely resembling evidence, nor has it had any actual calculated probabilities associated with it.

    PoNI:

    Watch out! (Winces as Bung caroms off the hood of a Subaru Outback.)

    Bung, with his dying breaths:

    You…wheeze…haven’t posted…gurgle…your calculations.

  21. Poor keiths. Just can’t keep up. And still trying pathetically to change the subject.

    Eyes. keiths. Focus.

    What is your initial estimate?

    It’s ok to admit you don’t have one.

    It’s ok to punt and say we don’t need any initial estimate that will be adjusted once we know more about the actual distribution.

  22. Mung,

    Please forgive me if I don’t trust your characterization of anyone else’s argument. Anyone’s argument, sadly. You have a rather bad track record in this regard – you even managed to mischaracterize YOUR OWN argument on this thread (“No, they are still rare” anyone?).
    Are you explicitly admitting that you mischaracterized Rumraket’s argument?
    Do you agree that the ubiquity and variety of distinct eye types across the animal kingdom leads to a reassessment of how unlikely eye evolution might be? That they are less unlikely than YOU originally thought?

    I really haven’t studied eye evolution in any detail. But it seems to me that eye evolution is plausible, at least — Darwin’s gradualism is supported by what we have learnt since Origin was written. If you want to argue that eye evolution is implausible, then the ball is in your court, mate.
    “If you actually have a probabilistic argument with regard to eyes I sure would love to hear it. What’s your best guess as to how improbable they are?”
    This is after all, the essence of the ID argument. And no, even if evolutionary theory isn’t quantitative enough to overcome your personal incredulity, it still remains the best explanation to date. But hey, produce something better.

  23. DNA_Jock: Are you explicitly admitting that you mischaracterized Rumraket’s argument?

    No. I’m saying that once he clarified his position I took his word that I misinterpreted his comment. [Something keiths never does.] Even Rumraket said he could see how I took it the way I did.

    But that’s a side issue. The main issue is how he’s arriving at his estimates. What are they based on?

    DNA_Jock: Do you agree that the ubiquity and variety of distinct eye types across the animal kingdom leads to a reassessment of how unlikely eye evolution might be? That they are less unlikely than YOU originally thought?

    OMG! Talk about mischaracterizing someone’s argument.

    How unlikely did I initially think eyes were. What was my original estimate? Quote me. Get keiths to quote me. He has it stashed somewhere I’m sure.

    Do you think it might ever sink in that my position is that we don’t know the probabilities? iirc I have stated that there are far more ways to be ‘not an eye’ than there are ways to be an eye. Is that what you’re thinking of? Do you find that position unreasonable?

    And no, even if evolutionary theory isn’t quantitative enough to overcome your personal incredulity, it still remains the best explanation to date. But hey, produce something better.

    Beautiful sentiment. But it has absolutely no impact on how probable or how improbable eyes are. So it’s really quite irrelevant.

  24. DNA_Jock: Darwin’s gradualism is supported by what we have learnt since Origin was written.

    Or not gradualism, that would be ok too.

    It’s not a problem for evolution as well. Nothing is. In fact, if we find out its not about gradualism, but rather about rapid change, we can change change our estimates. The theory now predicts it!

  25. Evolutionary theory predicts both that eyes are improbable and that eyes are not improbable. I think that’s what started this whole thing off. lol

  26. Mung: Posting gratuitous insults is for chumps.

    Only noticing when some posters post insults but not noticing others, is for Alan (and sometimes Neils).

  27. Here’s what I said earlier in the thread:

    Mung:

    Rumraket: If we have no knowledge (prior or otherwise) of the search space, assignment of probabilities is inappropriate.

    Then what was your calculation of the probabilities based upon?

    I think all this talk of the probabilities of the evolution of the eye are nonsense. Why don’t you?

  28. Also from upthread:

    Rumraket: Evolution is blindly and mindlessly sampling phenotypical space. And something that natural selection build into eyes was found at least 50 times independently.

    Now we can see where I got the idea that all Rumraket was doing was counting the number of times eyes evolved and not comparing that to anything else. (Such as the number of times eyes did not evolve, or that something else evolved.)

    From just counting the number of times that eyes evolved, what can we conclude with regard to the probabilties?

  29. My post to Rumraket:

    Mung: I have no idea what the probabilities are with respect to eye evolution, and neither do you. I don’t know how to calculate them, and neither do you. Not even using the frequentest interpretation.

    With coin tosses and tosses of a die you can calculate the probabilities. Show us how to do that with eye evolution.

    Are we clear on this DNA_Jock?

    I even included working links so that you can check to see if I am mischaracterizing my own statements. lol.

  30. Mung: (Such as the number of times eyes did not evolve, or that something else evolved.)

    Doesn’t matter, as long as there are more than 10, the number of times they didn’t evolve becomes irrelevant.

  31. Mung: With coin tosses and tosses of a die you can calculate the probabilities

    And with an infinite bag of balls, you only need ten to tell you what colors are inside.

  32. A frequentist view of probability is that it represents a long-run frequency over over a large number of repetitions of an experiment: if we say a coin has probability 1/2 of Heads, that means the coin would land Heads 50% of times if we tossed it over and over.

    – Introduction to Probability

    Even here the frequency is a relative frequency (Heads/Tails). Thus my harping on that missing element. Later Rumraket came around and agreed with me.

    Simply counting the number of times eyes evolved won’t do.

  33. I think some of this disagreement reflected the fact that “frequency” in statistics is sometimes used to mean the count of number of a particular type of event (as in “how frequently” it occurs), but in other fields such as population genetics, it means the fraction of all events that are of that type (as in “gene frequency”).

  34. Intuition 2.2.4 (frequentist interpretation). Recall that the frequentist interpretation of probability is based on relative frequency over a large number of repeated trials.

    – Introduction to Probability

    So once again, I was right. Go ahead and say it, keiths. Mung was right.

  35. Mung,

    Mung: A frequentist view of probability is that it represents a long-run frequency over over a large number of repetitions of an experiment: if we say a coin has probability 1/2 of Heads, that means the coin would land Heads 50% of times if we tossed it over and over.

    I don’t understand, why couldn’t he say more precisely, exactly how many times you need to toss it for it to land 50% of the time on heads. What if it never is 50% heads does that mean the probability was wrong? What if it is only 50% heads exactly once during the trial if you tossed it over and over, why do you only count the one time it was 50%, what about the time when it was 70% not heads?

    I am still waiting for keiths to tell me if each time you draw a black ball, the next time becomes more unlikely.

  36. phoodoo: I am still waiting for keiths to tell me if each time you draw a black ball, the next time becomes more unlikely.

    He’s waiting for you to go to sleep so he can refill the bag with more black balls.

  37. Joe Felsenstein: I think some of this disagreement reflected the fact that “frequency” in statistics is sometimes used to mean the count of number of a particular type of event (as in “how frequently” it occurs), but in other fields such as population genetics, it means the fraction of all events that are of that type (as in “gene frequency”).

    Boy, I think this really is going to get convoluted now. How frequently something occurs has a different meaning than the fraction of all events that are of a certain type?

    I think I can now see why the concept of fitness is so elusive.

  38. Mung: He’s waiting for you to go to sleep so he can refill the bag with more black balls.

    Based on his personality, I am willing to bet he has a whole bunch of blue balls.

  39. phoodoo,

    I am still waiting for keiths to tell me if each time you draw a black ball, the next time becomes more unlikely.

    I told you explicitly, but you were too dim to recognize it:

    If you sample with replacement, the probability of a black ball remains exactly the same each time you draw: 0.45. The probability of getting an all-black sample is therefore 0.45 raised to the tenth power.

    If you sample without replacement, then the probability changes ever so slightly with each draw. The probability of drawing ten black balls becomes

    45,000,000/100,000,000 * 44,999,999/100,000,000 * 44,999,998/100,000,000 * 44,999,997/100,000,000 … * 44,999,991/100,000,000 .

    Do the math.

  40. keiths,

    So let’s see how this applies to evolution. If we know of something happening only once, it is very rare, and we should never expect it to happen again. Like the evolution of intelligence to humans. Or like a peacock, that could never happen again.

    But if we know of something happening more than once, or like 50 times, that means it is easy to happen, very easy, and so we should expect to see it continuing to happen. Like eyes. Is that right?

    Now of course, if later, we find out intelligence evolves multiple times, like aliens on other planets, then it is no longer rare, and we should expect it to happen right? We just change our expectations and everything is cool again.

    I think I am getting it. So, since we have never found aliens, its virtually impossible. But later if we find them, then its likely.

    I think I got it.

    Thank goodness its impossible right now, I don’t want no aliens.

  41. phoodoo,

    Back to the goofy statement of yours that spawned this exchange:

    If there are 10 hundred, trillion, billion gazillion balls in a bag, and you only pull out 90, you have taken out so few, that its the same as only taken out 1-only worse.

    You got it completely wrong. Do you see that now?

  43. You see, phoodoo, if you draw one black ball, the frequency is 1. If you draw two black balls, the frequency is 2×1. If you draw three black balls, the frequency is 3×1.

    Do the math.

    It’s painfully obvious that keiths just doesn’t understand frequentist probability.

  44. phoodoo: But if we know of something happening more than once, or like 50 times, that means it is easy to happen, very easy, and so we should expect to see it continuing to happen. Like eyes. Is that right?

    So far only you and mung have characterized it as easy.Your odds are better with two tickets in the lottery than one, but It doesn’t make very easy.

    Design does not necessarily require a long time frame for designs to be implemented, shouldn’t we expect to see the design of eyes continuing to happen?

  45. phoodoo: I think I am getting it. So, since we have never found aliens, its virtually impossible. But later if we find them, then its likely.

    If we find aliens the probability that aliens exist is 1

  46. newton: If we find aliens the probability that aliens exist is 1

    Right! And that is just what Mung was explaining. And what’s the frequency Kenneth?

    I hate aliens, so I am so relieved, the frequency is zero and the probability is zero.

    Maybe, but I doubt it, DNA and keiths and Rum and Joe will start to see the problem.

  47. phoodoo: Boy, I think this really is going to get convoluted now. How frequently something occurs has a different meaning than the fraction of all events that are of a certain type?

    For an example of the use of “frequency” to mean the number of a certain type of event in a sample, see this web page.

    As long as we keep in mind in which sense “frequency” is being used, there is no confusion that results, but it is good to be aware that there is an issue, when you come to a new example.

    I think I can now see why the concept of fitness is so elusive.

    It is not elusive at all to those who use it in biological science. It is infinitely elusive to people who insist, for their own odd reasons, that it must be meaningless.

  48. Mung,

    But that extra information has to be relative to some other information in order for it to be useful in discovering the unknown actual frequencies and to help you refine your initial assessment.

    I don’t get this ‘relative’ thing. You are just sampling the bag. Your sample is the information, relative to nothing else.

    Oh, and you need an initial assessment in the first place.

    Well, yeah. Your initial assessment is that X is vanishingly improbable, if you are advancing one of the stock Creationist arguments.

  49. Mung,

    From just counting the number of times that eyes evolved, what can we conclude with regard to the probabilties?

    Not Impossible, for starters. That’s where this tends to come from – X Is Impossible Without Design. Ooh look, multiple X’s. “Yeah, but they’re all Impossible Without Design”. “Show your working”. “No, YOU show your working …”.

  50. I guess at some point we can forgive Allan for having been away and upon returning in jumping right in without knowing the context. But after seeing this over and over again it is starting to become a tad tiresome.

    I’ve not claimed that eyes are impossible without design. Nor has phoodoo. Nor has anyone else in this thread or the eye thread.

    I’ve also not made an initial assessment that eyes are vanishingly improbable. In fact i have explicitly denied making any initial assessment. Of course, if you’re not really participating in this thread you probably missed that.

    In fact, it is evolutionists who say the eye is improbable:

    Natural selection is not just a scientifically respectable alternative to divine creation. It is the only alternative that can explain the evolution of a complex organ like the eye. The reason that the choice is so stark – God or natural selection – is that structures that can do what the eye does are extremely low-probability arrangements of matter.

    Is anyone paying attention? Anyone?

    As a final point, I don’t think information can be information without being being relative to something else. I think you’re just making things up as you go.

    But when you don’t even know the proportions, pulling a second gives you extra information about what’s in the bag – you are getting closer to discovering the unknown actual frequencies, refining your initial assessment if based only upon the first.

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