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. Mung,

    Now increase the number of cards in the deck by one. Give it the same value and suit as one of the existing cards in the deck. Did that improve his odds of being dealt a straight flush? Only in evo-fantasy-land.

    Nope. Not even there. The first thing happening has no bearing on whether it will happen again, and no-one’s saying it does.

    However. Let’s try another analogy. You have a bag of balls. Some of them have an eye painted on. Your poker analogy has you knowing what the proportion of eye-balls is. You seem to think people are saying that pulling one eye-ball out increases the chance of pulling a second. Of course it doesn’t. 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.

    It’s also a bit like doing an experiment twice, and then a third time and so on. The first attempts don’t affect the outcomes of the later ones, they just keep sampling the (unknown) distribution.

  2. Tom English: However, we now treat the Devil’s own invention, sets, as more fundamental than the integers. The counting numbers 0, 1, 2, … are defined as sets:

    Erik: The line of thinking where you can derive other numbers from zero is parallel to that creatio ex nihilo makes sense.

    Are you not a linguist? I illustrated how a recursive definition of the natural numbers works, without giving the definition. My use of the familiar names 0, 1, 2, 3, … is only to aid understanding. Formally, the empty set {} is a natural number, and if n is a natural number, then the union of n and {n} is also a natural number.

    Erik: Either way, none of this is from the Devil. Why do you think it is?

    The Wikiquote translation of Kronecker: “God made the integers, all the rest is the work of man.” I thought it was somewhat humorous to say, when defining God’s invention in terms of sets, that sets are the Devil’s own invention.

  3. Allan Miller:
    Mung,

    Nope. Not even there. The first thing happening has no bearing on whether it will happen again, and no-one’s saying it does.

    However. Let’s try another analogy. You have a bag of balls. Some of them have an eye painted on. Your poker analogy has you knowing what the proportion of eye-balls is. You seem to think people are saying that pulling one eye-ball out increases the chance of pulling a second. Of course it doesn’t. 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.

    It’s also a bit like doing an experiment twice, and then a third time and so on. The first attempts don’t affect the outcomes of the later ones, they just keep sampling the (unknown) distribution.

    Exactly this. ^

  4. Tom English: I illustrated how a recursive definition of the natural numbers works, without giving the definition. My use of the familiar names 0, 1, 2, 3, … is only to aid understanding. Formally, the empty set {} is a natural number, and if n is a natural number, then the union of n and {n} is also a natural number.

    I know all that. The problem is that you are avoiding answering the ontological implications of mathematics (or arithmetic or set theory), if any. Neil is strongly anti-realist with regard to mathematics. You?

    Tom English: I thought it was somewhat humorous to say, when defining God’s invention in terms of sets, that sets are the Devil’s own invention.

    So you were just being funny. Here’s another funny quote for you, “God exists since mathematics is consistent, and the Devil exists since we cannot prove it.”

  5. Erik: Here’s another funny quote for you, “God exists since mathematics is consistent, and the Devil exists since we cannot prove it.”

    You’re right, that is hilarious.

  6. Allan Miller: You have a bag of balls. Some of them have an eye painted on. Your poker analogy has you knowing what the proportion of eye-balls is. You seem to think people are saying that pulling one eye-ball out increases the chance of pulling a second. Of course it doesn’t. 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.

    That’s subject to misreading. You’re not claiming to gain information about the proportion for the balls remaining in the bag. You’re addressing the proportion of the balls, drawn and yet-to-be drawn, that are eye-balls.

  7. Tom English,

    That’s subject to misreading. You’re not claiming to gain information about the proportion for the balls remaining in the bag. You’re addressing the proportion of the balls, drawn and yet-to-be drawn, that are eye-balls.

    OK, granted. The proportions that-were-in-the-bag. This is why I keep schtum! 🙂

  8. Rumraket: Exactly this. ^

    Yea, you would believe that this analogy applies to evolution, wouldn’t you Rum? Is the bag finite? Do you know how many are in the bag to start with? Why would pulling anything out of the bag tell you what is remaining in the bag, if you don’t know how many kinds of things, or how much was in the bag to begin with?

    What you have pulled out tells you absolutely zero about the frequencies inside remaining, if you never know how many there were. If you pulled out ten, how do you know there isn’t a billion inside? So you pulled out 7 red things and 2 blue things, do you know anything about what else is inside? If you pulled out 1000, how do you know there isn’t 10*25 things inside?

  11. Erik: The problem is that you are avoiding answering the ontological implications of mathematics (or arithmetic or set theory), if any. Neil is strongly anti-realist with regard to mathematics. You?

    Avoiding? I don’t care enough to avoid.

  13. Erik: The problem is that you are avoiding answering the ontological implications of mathematics (or arithmetic or set theory), if any.

    There are no ontological implications.

  14. Allan Miller: The first thing happening has no bearing on whether it will happen again, and no-one’s saying it does.

    Independent events. Congratulations. And what happens to the probabilities given independent events?

  15. Rumraket: I see that you fail to distinguish frequentist from prior probabilities.

    I see that you’ve forgotten [abandoned?] your original claim.

  16. Tom English: Do you believe that complete absence of knowledge of a process with a finite number of outcomes compels you to regard the outcomes as equiprobable?

    No. I would not go so far as to say that complete absence of information compels anyone to adopt that assumption.

    Tom English: Hint: If you know nothing, then how do you justify assigning probabilities to outcomes?

    And you know that I know that DEM didn’t just make that up. How do I justify it? The same way that other people who use that technique justify it. IIRC, it even has a name.

  17. Tom English: In all honesty, Mung, I have gone from the presumption that they knew more than I did about the subject matter — especially probability and information — to the realization that they’re pretending to be experts on subjects they know poorly.

    You can be certain that I know less than you. 🙂

  18. Erik: The problem is that you are avoiding answering the ontological implications of mathematics

    What about number 666? Why didn’t mathematicians skip that one?

  19. phoodoo: Yea, you would believe that this analogy applies to evolution, wouldn’t you Rum? Is the bag finite? Do you know how many are in the bag to start with? Why would pulling anything out of the bag tell you what is remaining in the bag, if you don’t know how many kinds of things, or how much was in the bag to begin with?

    It doesn’t, it tells you something about what was in the bag. When you pull out an eye, you know the there is was at least one eye in the bag when you pull out the second you know were at least two, buying two lottery tickets make the odds of a improbable event more probable than buying one.

  21. Tom English: Do you believe that complete absence of knowledge of a process with a finite number of outcomes compels you to regard the outcomes as equiprobable?

    DEM:

    Bernoulli’s PrOIR is applied in the examples of active information in Chapter 5.4.2. The definition of active information, however, need not use a uniform distribution as a baseline, but can measure added information from any distribution. The idea is the same as measuring dB (decibels) which, like active information, is proportional to the logarithm of a ratio. The denominator of the ratio, the reference, can be any value desired.

  22. He asked you, Mung, not DEM.

    Why? Because you are the one presenting the following as if it were analogous to evolution:

    If we had a deck consisting of only five cards, and we dealt Rumraket a poker hand that gave him a straight flush. Shuffled the deck, dealt again, and lo and behold another straight flush. How many in a row would it take him before he figured out that being dealt one straight flush after another didn’t increases his chance of getting yet another one in the slightest. What’s the over and under?

    Now increase the number of cards in the deck by one. Give it the same value and suit as one of the existing cards in the deck. Did that improve his odds of being dealt a straight flush? Only in evo-fantasy-land.

    This topic is way above your pay grade.

  23. Mung: I see that you’ve forgotten [abandoned?] your original claim.

    No, I have not. Everything I’ve said is still exactly as I said it.

  24. Mung: Independent events. Congratulations. And what happens to the probabilities given independent events?

    Again confusing prior vs frequentist probability.

    This really is your problem. Learn the distinction.

  25. Rumraket: Again confusing prior vs frequentist probability. This really is your problem. Learn the distinction.

    Snore.

    Frequentists argue that with no prior knowledge of the search space, assignment of probabilities is inappropriate and falls outside of the scope of probability theory.

    – Introduction to Evolutionary Informatics

    Are you saying they are wrong?

  26. Mung: Rumraket: Again confusing prior vs frequentist probability. This really is your problem. Learn the distinction.

    Snore.

    Frequentists argue that with no prior knowledge of the search space, assignment of probabilities is inappropriate and falls outside of the scope of probability theory.

    – Introduction to Evolutionary Informatics

    Are you saying they are wrong?

    No with that statement I absolutely agree. If we have no knowledge (prior or otherwise) of the search space, assignment of probabilities is inappropriate.

  27. 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. newton: When you pull out an eye, you know the there is was at least one eye in the bag

    Right, we know eyes exist. How does that help us?

  29. Mung: 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?

    Because we have information about the search space. Eyes have evolved independently at least 50 times (IIRC). There is scarcely a macroscopic animal living in daylight on our planet that doesn’t have eyes. This tells us that eyes are extremely beneficial, so much so that organisms without them almost universally go extinct, or move to a low-light/lightless niche.

  31. Mung: Please inform Tom that evolution is search.

    We can dispense with the word search if you find it unsettling Mung. I’ve already informed you before that I’m not obsessed with labels for concepts and processes of various kinds.

    As long as we are clear that there is no evidence that there is deliberation, or intention, or intelligence behind it, then I’m fine with calling it (the random sampling in evolution) a search. So it is metaphorically, not literally, a search.

  32. Rumraket: We can dispense with the word search if you find it unsettling Mung.

    You’re hilarious. Your position depends on you having information about the search space. Your words. Try making your argument without it.

  33. Calling it “phenotypical space”, instead of “search space” would also be just fine with me. I think that’d be okay with Tom.

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

  34. Mung: You’re hilarious. Your position depends on you having information about the search space. Your words. Try making your argument without it.

    Phenotypical space.

    That wasn’t so hard.

  35. Rumraket: Phenotypical space.

    That wasn’t so hard.

    LoL. Phenotypical space is the space of what? All possible phentypes? All known phenotypes? Now see if you can connect that with your frequentist interpretation of probability argument.

  36. Mung,

    What are we going to call the space in between phenotype space?

    Dam, I wish Stephen Jay Gould were still around, he could come up with something catchy.

  37. Rumraket: Calling it “phenotypical space”, instead of “search space” would also be just fine with me. I think that’d be okay with Tom.

    Yup.

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

    Emphasis added. Sampling is the word I like best. Natural selection, as differential reproduction of types of organism defined in terms of heritable traits, is biased sampling of the space of types. That’s not the whole story. And I’m not pretending to be a theoretical biologist. But biased sampling of types is something that generally occurs when there is a population of reproducing organisms.

    You say that you’re not hung up on terminology. That’s fine. But it’s crucial to ID that the rank and file take terms like search at face value. Mung is not idiosyncratic in his insistence that “searches” really do search. So I ask, if you have a natural, technically correct, and teleology-free term like sampling to use, then why use a term that you know is the source of a lot of misunderstanding?

    In generic terms, the space that is sampled is the sample space. Dembski and Marks in fact used that term in their early papers. I was surprised that they’d missed an opportunity for terminological begging of the question, search space. Now virtually all of their terminology assumes the conclusion that they are supposed to establish, namely that the processes under consideration are designed to serve purposes.

    To be sure, I have my own computer-scientist reasons for preferring the term sampling. The most important of them is that the “no free lunch” theorems for search/optimization actually address sampling (without replacement, as in Allan’s example above). When I added a preface to my first NFL paper, explaining why I was wrong to have spoken of “conservation of information,” I gave it the title “Sampling Bias Is Not Information” (blogged here). Now Marks et al. write that the Law of Conservation of Information is “illustrated” by the “no free lunch” theorem for search. If you allow that the algorithms under consideration search for a solution to a problem, then it seems “obvious” that their differences in performance are due to information. But, if one accepts that the algorithms in NFL are actually samplers, then it is clear that they differ in their biases, not their information.

    By the way, if Marks et al. were operating as legitimate researchers in engineering, then they would model the agent that selects a sampler. It is the sampler-selecting agent, not the sampler, that possibly exploits information. The notion that the information is literally present in phenomena themselves, and can be measured objectively, goes back to Dembski’s The Design Inference. As for the line you’ve been taking on frequentist versus subjectivist interpretations of probability, it’s hugely important, because Dembski has gone from advocating Fisherian statistics and bashing Bayesianism (he devoted a chapter to it in one of his books — The Design Revolution?) to championing Bernoulli’s Principle of Insufficient Reason, which addresses subjective assignment of probability.

    Mung: DEM:

    Bernoulli’s PrOIR is applied in the examples of active information in Chapter 5.4.2. The definition of active information, however, need not use a uniform distribution as a baseline, but can measure added information from any distribution. The idea is the same as measuring dB (decibels) which, like active information, is proportional to the logarithm of a ratio. The denominator of the ratio, the reference, can be any value desired.

    The baseline is subjective. Their carrying on about Bernoulli is nothing but an attempt to make a subjective assignment of probability seem logically necessary, and hence objective. It’s a sleazy game. Active information is not an objective measure.

  39. Mung,

    Independent events. Congratulations. And what happens to the probabilities given independent events?

    Not clear what you are actually asking here.

  40. Tom English: Emphasis added. Sampling is the word I like best. Natural selection, as differential reproduction of types of organism defined in terms of heritable traits, is biased sampling of the space of types. That’s not the whole story. And I’m not pretending to be a theoretical biologist. But biased sampling of types is something that generally occurs when there is a population of reproducing organisms.

    You say that you’re not hung up on terminology. That’s fine. But it’s crucial to ID that the rank and file take terms like search at face value. Mung is not idiosyncratic in his insistence that “searches” really do search. So I ask, if you have a natural, technically correct, and teleology-free term like sampling to use, then why use a term that you know is the source of a lot of misunderstanding?

    In this particular instance I was responding to Mung’s quoting DEM, so I just went with the term they used. I hate to quibble about words as I think it’s silly and I keep making this assumption that people discussing this subject have been around long enough to understand what biologists mean when they use words like design, search and so on.

    But it’s true with this particular audience, we have to constantly police our language and clarify what we mean, otherwise IDists get their knickers in a twist when they read words like ‘code’, ‘design’, ‘creation’, ‘seach’, etc.

  42. Chortle. my bag of balls model appeared to be sampling-without-replacement (it wasn’t in my head, but I accept that’s how it appeared). So let’s attack that, because that’s not what happens in evolution! There is absolutely NO variant model comes to mind that could make it more appropriate … such as .. ummm … no, stumped.

    This is the fascinating thing about all these debates – the writhing that goes on in fields not directly related to evolution as soon as some relation to evolution is discovered. Happens with computing, with probability theory and statistics, genetics, standards of inference, chemistry and so on. No idea how the cognitive dissonance is dealt with internally.

  43. Allan Miller: Chortle. my bag of balls model appeared to be sampling-without-replacement (it wasn’t in my head, but I accept that’s how it appeared).

    But it was not supposed to be analogous to the process of evolution. The balls in a bag model is supposed to merely convey how it is that we can make statements about the probabilities of finding certain items in the bag, by sampling it.

  44. Rumraket: But it’s true with this particular audience, we have to constantly police our language and clarify what we mean, otherwise IDists get their knickers in a twist when they read words like ‘code’, ‘design’, ‘creation’, ‘seach’, etc.

    I’ve acquired a habit of worrying about how I will be misconstrued. It’s a fucking waste of time and energy. I already had a very hard time writing, due to ADD. This added concern has made things much worse. I think of it as brain pollution.

    So, while I have ideas about how best to deal with IDers, I also have my doubts as to whether it’s worth the cost.

    Allan: I wasn’t criticizing you when I stepped in, above. It was my chronic “how will this be misconstrued” scrutiny.

  45. Allan Miller: You seem to think people are saying that pulling one eye-ball out increases the chance of pulling a second. Of course it doesn’t. But when you don’t even know the proportions, pulling a second gives you extra information about what’s in the bag

    Allan Miller: Chortle. my bag of balls model appeared to be sampling-without-replacement (it wasn’t in my head, but I accept that’s how it appeared).

    So I actually did not understand what you were saying. Your comment makes more sense now, knowing that you were sampling with replacement. (The results of the draws are independently and identically distributed.) Beside saying something about replacement, you should refer to a second draw, instead of a second ball.

  46. Allan Miller: I’m betting people can see teleology in sampling too …

    Of course. What Marks et al. call blind search is uniform random sampling with replacement. In the first and second of their three definitions of active information, uniform random sampling without replacement has greater active information than “blind search.” They originally billed active information as a measure of teleology, but seem to have let go of that notion.

  47. Mung: Independent events. Congratulations. And what happens to the probabilities given independent events?

    You need to unlearn “independent events.” I assumed for years that Dembski knew something that I did not. He did not.

    Scientists sometimes speak of independent events. But the term has no meaning in probability theory.

  48. Tom English,

    Allan: I wasn’t criticizing you when I stepped in, above. It was my chronic “how will this be misconstrued” scrutiny.

    No, I got that, and phoodoo demonstrated your point admirably.

  49. Allan Miller: I’m betting people can see teleology in sampling too …

    Rumraket claims to have knowledge about the “sample space.” So yes.
    If eyes have evolved, then even more eyes will evolve.

  50. Mung: Rumraket claims to have knowledge about the “sample space.” So yes.
    If eyes have evolved, then even more eyes will evolve.

    No, not “if eyes have evolved then even more will evolve”. Nobody has claimed this anywhere.

    You’re confused again. We infer a probability from observation, instead of making up a probability a priori. If we observe that eyes only evolved once, then that is their frequency. If we observe they evolved twice, then their frequency is twice what it was if they only evolved once. They then seem to be twice as likely. And if they seem to have evolved three times, then they will have thrice the frequency of they did if they evolved once. And so on.

    Nobody says “eyes evolved once, so they will evolve twice, or three times or even more”.

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