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. Joe Felsenstein: I think we’re in agreement on the SfS. As far as the statistical theory goes, the performance in the Steiner Tree case is simple to deal with if we choose instances of the ST problem independently from the same distribution, such as sets of 100 points randomly chosen in a unit square. The measure of performance, the total length of the ST found, is bounded below (by zero) and above (loosely, by 100\sqrt{2}) so it has no ill-behaved “heavy tails”. All moments are finite. So the statistical behavior is rather simply analyzed.

    Do you recall how Fisher information fits into the picture? I won’t be taking the time, just now, to refresh myself.

  2. Tom: Fisher information is the expected value of minus the curvature of the log-likelhood. For a single random variable it would be the reciprocal of the asymptotic variance of the variable. So a big variance means a small information. There is a straightforward extension to multiple variables.

    In this case I am not sure we can easily compute the requisite log-likelihoods.

  3. Tom English: But I have to emphasize that evolutionary models are not evolutionary searches for solutions to problems. The biggest problem I have is conveying the difference in plain language.

    It may be easier to convey the difference by presenting it from the other direction: it should be clear to people that someone using a genetic algorithm to design a circuit board is not simulating the mating habits of circuit boards.

  5. J-Mac,

    I suspect that you don’t get my point.

    DEM say:

    [T]he fundamentals of evolutionary models offered by Darwinists and those used by engineers and computer scientists are the same.

    This is a fundamental misconception.

    The genetic algorithms used by engineers and computer scientists are not models of real-world processes, they are just algorithms. It’s the same as with simulated annealing algorithms; people who run them to design circuit boards are not modeling the way circuit boards solidify out of a liquid. (And the engineers and computer scientists understand all of this.)

    DEM are conflating process models and optimization algorithms.

    If you want a process model to give you insights about the behavior of a real-world process, then the steps in your process model have to be realistic enough to justify whatever insights you think you are getting. An optimization algorithm isn’t meant to give you insights into a real-world process, so the steps in the algorithm don’t need to correspond to those of a real-world process.

    I agree with Tom and I’m offering another way to explain what he is saying.

  6. Freelurker: It may be easier to convey the difference by presenting it from the other direction: it should be clear to people that someone using a genetic algorithm to design a circuit board is not simulating the mating habits of circuit boards.

    Turning things around is a good idea. Considering whether the approach would work is useful, even though the conclusion is that it would not.

    The scientific models that Marks et al. analyze as engineered searches are Avida-EQU and Schneider’s ev. I plan to focus on the former. Although Avidians are programs in a Turing-complete language, Marks et al. represent them as combinational circuits. They are saying, basically, that Avida would not have designed circuits unless it had been designed to design them. (They speak of Avida as though it were the particular experiment, rather than an experimental platform.)

    Hmm… I’ve just realized that Marks et al. are saying not only that ev searches, but also that it searches for the design of a perceptron along with a sequence of bases processed correctly by the perceptron. (Now I understand why they believe that Schneider “smuggled in information” by supplying the structure of the perceptron.) So, again, ev would not have designed a perceptron unless Schneider had designed ev to design a perceptron. I’m thinking now that I should not ignore ev.

    Marks et al. also address Ray’s Tierra, but do not treat it as an engineered search. They don’t say that Tierra seeks a target. Yet they say that Tierra does not “work.” I say that if they can say that Tierra does not work, then they must have a “target” vaguely in mind. I’m putting “target” in scare quotes because there is no more a problem to be solved in ev and Avida-EQU than in Tierra. That’s a difficult point to explain. But I’m thinking now of trying to explain it.

    I can’t tell you what will come of this. Sometimes I write an explanation three or four or five different ways, and then conclude that I don’t know how to make it clear. But you’ve helped me make some connections I hadn’t made before. So thanks for the comment.

  7. Tom English: When we express observations in mathematical language, our observations are not reality itself, and our mathematical expressions of our observations are not reality itself. There might be something wrong with our observational apparatus, and there might be something wrong with what we say about — our expressions of — the observations made with the apparatus.

    Unless you are talking about quantum mechanics; i.e. double-slit experiment observations, it is a contradiction…makes no sense to me…

    Maybe “Evo-Info Evolution is not Seach” has run its course and is searching again…

    I agree with Mung…This OP has run its course…

  8. J-Mac: I agree with Mung…This OP has run its course…

    I agree with Alan Fox. You should address moderation issues, e.g., the criteria for featuring a post, on the moderation page. Personally, I think that posts parodying other posts should be featured parodically. And what would parodic featuring of a parody entail, other than to stick it at the very bottom of the page? But, again, these are moderation issues.

    I’ll repeat Alan’s invitation to Bob Marks, and promise to stick to technical issues.

    Evolutionary informatics is founded on the false conflation of evolutionary models and evolutionary search. I have made it clear that evolution is not, in and of itself, search. Thus the notion that “information makes evolution possible,” at the heart of evolutionary informatics, is bunk.

  9. Mung: It had been sitting for almost three weeks without any activity whatsoever.

    <b<Tom English:

    Mung addressed the issue here…

    Your response doesn’t seem to suggest you were interested in this issue to be resolved in the Moderation Issues

    Instead, you wrote a long and pretty obnoxious response…

    In the end, I agree this is a moderation issue theme….

  11. J-Mac,

    You didn’t actualy repond to my question:

    Tom English: When we express observations in mathematical language, our observations are not reality itself, and our mathematical expressions of our observations are not reality itself. There might be something wrong with our observational apparatus, and there might be something wrong with what we say about — our expressions of — the observations made with the apparatus.

    Unless you are talking about quantum mechanics; i.e. double-slit experiment observations, it is a contradiction…makes no sense to me…

    Can you elaborate please

  15. Tom English: Evolutionary informatics is founded on the false conflation of evolutionary models and evolutionary search. I have made it clear that evolution is not, in and of itself, search. Thus the notion that “information makes evolution possible,” at the heart of evolutionary informatics, is bunk.

    So what would your response be if evolutionary informatics were founded on the evolutionary model that stipulated mutations to be non-random, but rather governed by quantum mechanics?

  16. Tom English: Evolutionary informatics is founded on the false conflation of evolutionary models and evolutionary search. I have made it clear that evolution is not, in and of itself, search. Thus the notion that “information makes evolution possible,” at the heart of evolutionary informatics, is bunk.

    J-Mac: So what would your response be if evolutionary informatics were founded on the evolutionary model that stipulated mutations to be non-random, but rather governed by quantum mechanics?

    Thanks, at least, for moving in the direction of the OP. Whether or not quantum mechanics is random is a matter of interpretation. Most physicists favor interpretations in which randomness is physically real. So your question is strange. In any case, evolutionary informatics is (1) analysis of search (2) misapplied to evolutionary models. Marks, Dembski, and Ewert do not provide a model of evolution. You’re essentially asking me, “What if evolutionary informatics were what it is not?”

    Have you read the preface and the introduction to the book? They’re both available online. Click on the title of the book, at the top of my post.

  17. I finnly got through all the details of the Evo-Info 3: Evolution is not search and some other stuff related to Tom English’s claims…
    OMG!!! What a boring theme! I don’t think I have ever read anything scientific as boring as this…maybe with the exception of Deepak Chopra’s book “You are the Universe”

    Well, I gotta tell you, I have a lot of admiration for people who can spend more than 5 minutes on the theme every day…

    Anyways, Tom English’s premise (which I already questioned in my earlier comments) is rather surprisingly simple; He doesn’t like the idea that:

    “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.” because at the very end of it implies information and the source of it as ID, to make the long and unnecessary story short…
    So, what’s Mr. English’s solution to the problem?

    Easy…All you need is specifically fine-tuned laws of physics for evolution process of random mutation and natural selection, and genotypes that have fitness and voila…It could not be any easier…

    Who can argue with that…

    I think I will be speaking for few people here, that it is our hope that the next episode of Evo-Info 4 will contain the information on not only how the laws of physics came to be, but what or who did the search for the just right fine-tuning of the cosmological constant to be 10 to 120 that makes Mr. English’s evolution without search even possible…

    After that’s resolved the appearance of genotypes that have fitness should be a piece of cake for Mr. English or his buddy Joe Felseinstein… lol

    Good night!

  18. Tom English: Whether or not quantum mechanics is random is a matter of interpretation. Most physicists favor interpretations in which randomness is physically real.

    Obviously, there is randomness in QM and I am the first one to claim it…However, I don’t think you understand what you are talking about…
    How could quantum mechanics govern many processes that depend on non-randomness such as mitosis…if it were totally or even 50% random? If there were true, you wouldn’t survive reading to the end of this comment…Do you realize how ridiculous your statement is? No wonder you’d thought my question was strange…
    I’d suggest you look it up or speak to the physicists who interpret quantum mechanics as it is…
    BTW: Maybe you can also explain what your favorite physicist mean by when they say “randomness is physically real.” No offense but the only alternative I could think of was randomness that is physically unreal…Maybe you physicists should not be reading nonsense blogs and tell you to repeat it…lol

  19. Tom English: In any case, evolutionary informatics is (1) analysis of search (2) misapplied to evolutionary models. Marks, Dembski, and Ewert do not provide a model of evolution. You’re essentially asking me, “What if evolutionary informatics were what it is not?”

    I wrote about this in my previous comment 4:15 am.
    Why would they provide a model of evolution at all if it doesn’t fit their premise in the first place? Don’t you think this is a strange question? Would they expect you to provide a model for the creation of a cell if they knew, you didn’t believe in creation and ID? Yes? No? Why?

    Have you read the preface and the introduction to the book? They’re both available online. Click on the title of the book, at the top of my post.

    I have…So?

  20. J-Mac: How could quantum mechanics govern many processes that depend on non-randomness such as mitosis…if it were totally or even 50% random?

    The same way quantum mechanics could govern processes such as rocks rolling down a hill. Which it does.

    Quantum mechanics also governs all chemical reactions, including those involved in mutation.

    Forget biology, read elementary physics and elementary chemistry to understand that. And if you don’t “get it” after reading that, go bother the physicists and chemists and not us.

  21. J-Mac,

    I think I will be speaking for few people here […]

    Here it is again – the gift that keeps on giving! I am a small, small man in many ways.

  23. J-Mac: I don’t think I have ever read anything scientific as boring as this…maybe with the exception of Deepak Chopra’s book “You are the Universe”

    I’d love to see what else is on your science shelf.

  25. J-Mac: How could quantum mechanics govern many processes that depend on non-randomness such as mitosis…if it were totally or even 50% random? If there were true, you wouldn’t survive reading to the end of this comment…

    I wonder what you think “random” means.

    The economy of Las Vegas is built on randomness. Somehow casino operators manage to make a fortune out of randomness.

  26. J-Mac: Why would they provide a model of evolution at all if it doesn’t fit their premise in the first place?

    If they were scientists, they would be driven by curiosity, not by belief. Disproving a favored belief can be good science and can be very satisfying to the curious.

  27. J-Mac: Why would they provide a model of evolution at all if it doesn’t fit their premise in the first place?

    You have a point, why would they bother with an honest test of evolution when they’re IDists?

    It’s not like IDists typically deal with evolution in a straightforward manner.

    Now if they were scientists interested in the truth…

    Glen Davidson

  29. : Tom English: In any case, evolutionary informatics is (1) analysis of search (2) misapplied to evolutionary models. Marks, Dembski, and Ewert do not provide a model of evolution.

    Well, who does provide a model of evolution?

  30. Tom English: In any case, evolutionary informatics is (1) analysis of search (2) misapplied to evolutionary models. Marks, Dembski, and Ewert do not provide a model of evolution.

    phoodoo: Well, who does provide a model of evolution?

    All of your sass, and in the end it comes to light that you have not bothered even to read the preface to the book. I guess I should have known.

  31. Joe Felsenstein: The same way quantum mechanics could govern processes such as rocks rolling down a hill.

    I have quantum mechanics working on my car full time. It’s expensive but worth it.

  35. phoodoo: Well, who does provide a model of evolution?

    And why is it relevant, given that DEM are talking about specific models or types of models.

  36. Tom English:
    All of your sass, and in the end it comes to light that you have not bothered even to read the preface to the book. I guess I should have known.

    Huh, the preface to their book?

    I am asking you what model you think is a model of evolution? I should refer to their book?

  39. Mung,

    Neil already won the keiths award for today. Could you post this again tomorrow? It’s a sure winner.

    What can I say? I’m a small, small man in many ways.

  43. keiths:
    He will probably stare at that and have no idea what you’re talking about.

    So, you tell us since you seem to be doing all the laughing…!

    I bet you are going to wait for someone else, more than few people, to confirm or deny it before you are going to repeat it…

  44. J-Mac: Why don’t you tell us what randomness is and I will tell you what randomness is as per QM…

    For me, randomness is what can be modeled by the mathematical theory of probability.

    Note that probability theory includes theorems, so it should not be surprising that one can have physical laws where randomness is involved.

  45. J-Mac:

    I think I will be speaking for few people here […]

    Allan:

    Here it is again – the gift that keeps on giving! I am a small, small man in many ways.

    keiths:

    He will probably stare at that and have no idea what you’re talking about.

    J-Mac:

    So, you tell us since you seem to be doing all the laughing…!

    As predicted. And he can’t even figure out that Allan is laughing at him, too. (And quite a few others are laughing too, I suspect.)

  46. The things I chuckle at, J-Mac, are the inadvertent slips that mean the opposite of what you intend. I wouldn’t mention it at all but for the fact that your style is generally somewhat contentious, which (me being human and all, and, I freely admit, a big kid) makes it all the funnier.

  49. Allan Miller: I know what reaction I’d get off my kids if I tried to get them to wade through this lot …

    They would look at you funny and try to have you committed?

    😉

  50. Mung,

    They would look at you funny and try to have you committed?

    They already look at me funny. My son in particular has a little mime he does when he catches sight of the ‘penguin’ page header on my computer – someone vigorously attacking a keyboard, muttering angrily! He’s a biology graduate, but no interest in this kind of discussion.

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