Evo-Info 3: Evolution is not search

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,  = 2 ⨉ .005 = .01 for the blue process, and  = 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  = .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 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.

832 thoughts on “Evo-Info 3: Evolution is not search”

  1. colewd

    Allan Miller,

    I wonder if a spell in the sciences is a factor here. Chucking quadrats around, mark-release-recapture, etc – the principles seem pretty unexceptionable, until the spectre of evolution raises its bony hand.

    This works just fine if your population size is solidly finite.

  2. Alan FoxAlan Fox

    colewd: This works just fine if your population size is solidly finite.

    Accepting for the moment that statistics works only with finite quantities, why do we need to worry about infinite populations? Are there such things?

  3. John HarshmanJohn Harshman

    Why wouldn’t it work with an infinite population? Or does Bill just not have a filter?

  4. keithskeiths

    John,

    Why wouldn’t it work with an infinite population?

    No reason that I can see. Bill, why do you think it would be a problem?

  5. keithskeiths

    Rhetorical question: Why do so few IDers understand the basics of evolution and probability/statistics, when those are precisely the subjects upon which their (flimsy) arguments depend?

  6. MungMung

    Allan Miller: Why are you flipping a coin to find out how many sides it has? Can’t you just look?

    Not sure why I’d need to look at an actual coin when I can just read a book about probability.

  7. colewd

    Alan Fox,

    Accepting for the moment that statistics works only with finite quantities, why do we need to worry about infinite populations? Are there such things?

    What do you think is the population size of eyeballs vs no eyeballs? If we are observing a successful selection of eyeballs and an almost infinite population size what do you think that tells you?

  8. RumraketRumraket

    colewd:
    Alan Fox,

    What do you think is the population size of eyeballs vs no eyeballs?If we are observing a successful selection of eyeballs and an almost infinite population size what do you think that tells you?

    Bill please explain what the hell this is even supposed to mean. Population size of eyeballs?

    Do you even know what is being discussed in this thread?

  9. RumraketRumraket

    Mung: Not sure why I’d need to look at an actual coin when I can just read a book about probability.

    Why do anything at all when you already know all the answers you believe can’t be wrong?

  10. Allan Miller

    Mung,

    Not sure why I’d need to look at an actual coin when I can just read a book about probability.

    No, I still think looking at the coin would be best.

  11. Allan Miller

    colewd,

    What do you think is the population size of eyeballs vs no eyeballs? If we are observing a successful selection of eyeballs and an almost infinite population size what do you think that tells you?

    Almost infinite? That’s almost nothing! Almost infinite is infinitely less than infinite.

    Still, you too seem to be running away with the idea that every statement about probability is a statement about evolution.

  12. MungMung

    Allan Miller: No, I still think looking at the coin would be best.

    Now we have machines that can look at our coins for us. 🙂

    I recently processed a bunch of coins through a Coinstar machine. It actually rejected a silver quarter that I had mixed in.

  13. dazzdazz

    KairosFocus and his “largest known number”
    Bill Cole and his “number so large that it’s an almost infinite number, an imaginary number”
    Phoodoo and his “orders of magnitude”

    Creationist minds vs math, no contest

  14. GlenDavidson

    dazz:
    KairosFocus and his “largest known number”
    Bill Cole and his “number so large that it’s an almost infinite number, an imaginary number”
    Phoodoo and his “orders of magnitude”

    Creationist minds vs math, no contest

    It’s like biology, creationists only need to know that math was designed by God the Designer.

    Understanding is pointless, possibly a sin.

    Glen Davidson

  15. MungMung

    petrushka: For one thing, the largest known number would be almost infinite.

    I think Allan’s point is that there’s no such thing as “almost infinite.”

  16. MungMung

    DNA_Jock: I was motivated by my desire to describe a situation in which the probabilities have changed.

    Yes, I agree that would change the probabilities. Remind me again how this supports the claim by keiths that this is all about epistemic probabilities. It would change the probabilities for me. It would change the probabilities for you. If not why not.

  17. MungMung

    DNA_Jock: One does not need to be able to estimate the probability of an event in order to be able to describe situations in which the probability has increased or decreased.

    ok, yes. I agree. If you have a deck of 52 cards and you add 10 more cards to the deck, all of which are spades, the probability of drawing a heart will decrease even if you didn’t know the probability of drawing a heart in the first place.

  18. DNA_Jock

    Mung: ok, yes. I agree.

    Very good, Mung. You learned something about probabilities today — when you originally disagreed with this statement, you were wrong.

    If you have a deck of 52 cards and you add 10 more cards to the deck, all of which are spades, the probability of drawing a heart will decrease even if you didn’t know the probability of drawing a heart in the first place.

    Well, there is one subtlety here: in order to know that the probability has decreased, you would need to know that there was at least one heart in the deck. Conversely, if we added hearts to the deck, in order to know that the probability has increased, you would need to know that there was at least one non-heart in the deck. Do you follow this?
    More importantly, you do NOT need to know how many cards are in the deck. So long as the deck is finite, the number of cards in the deck is irrelevant to knowing whether the addition of a single card raises or lowers the probability of drawing a heart.
    What was the point of all this brouhaha? Two-fold: 1) to advance your education re probability, and 2) a demonstration of Allan Miller’s point that “…some see every statement made about probability as being a statement about evolution. And therefore to be resisted at all costs. ”
    It’s been interesting.

  19. MungMung

    DNA_Jock: Well, there is one subtlety here: in order to know that the probability has decreased, you would need to know that there was at least one heart in the deck. Conversely, if we added hearts to the deck, in order to know that the probability has increased, you would need to know that there was at least one non-heart in the deck. Do you follow this?

    Yes I understand it. It was,in fact, the basis for my disagreement with you. I considered once again rewriting your comment to the following:

    One does not need to be able to estimate the probability of an event in order to be able to describe situations in which the probability has changed.

    I thought you were saying that you could say with specificity what the actual direction of change was relative to the former state. If your claim was merely that we could know the probabilities changed, then why didn’t you say that and save us a lot of trouble?

    More importantly, you do NOT need to know how many cards are in the deck. So long as the deck is finite, the number of cards in the deck is irrelevant to knowing whether the addition of a single card raises or lowers the probability of drawing a heart.

    I agree. And I don’t believe in a deck of cards that is infinite, so I assumed we were both talking about a finite deck. 🙂

    …when you originally disagreed with this statement, you were wrong.

    I find it odd that you should think so. You actually seem to have agreed with me.

    …in order to know that the probability has decreased, you would need to know that there was at least one heart in the deck.

    That’s what I said. Or at the very least, that’s what I meant.

    Conversely, if we added hearts to the deck, in order to know that the probability has increased, you would need to know that there was at least one non-heart in the deck.

    That’s what I said. Or at the very least, that’s what I meant.

    On what basis do you think I was disagreeing with your original statement, if not this? Were you trying to follow the logic of my objection, or just assuming there was none?

  20. MungMung

    Well DNA_Jock. On the bright side, you’re posting habits are nothing like mine, which should simply the search for your comments and my responses. I’ll see if I can’t reconstruct the trail so that we can have some way to judge whether or not I was right all along and you just misread what my objection was.

    Since I say that it was you who misjudged, I’ll take on the burden of trying to show how.

  21. DNA_Jock

    I can give you a recap.
    The statement:

    One does not need to be able to estimate the probability of an event in order to be able to describe situations in which the probability has increased or decreased.

    Mung

    I disagree. If you are going to claim that some probability has changed, you need to know what it is that you’re talking about that has allegedly changed. Else you won’t know by which direction it changed.

    DNA_Jock offers up scenario 1:

    I present you with a well-shuffled deck of cards, and ask you “What’s the probability that you draw a heart from the deck?”
    And the answer is “I don’t know”.
    Awesome!
    Next, I remove a card from the deck, and show it to you — it’s the ten of hearts — and burn it. I also show you the seven of spades, but return that card to the deck.
    Now I ask you two more questions:
    1) “What’s the probability that you draw a heart from this deck?”
    2) “Has the probability decreased since I first asked you?”
    Now, if you are being honest, your answers will be “I don’t know” and “Yes, the probability has gone down”
    Now might be a good time to re-evaluate your disagreement with the statement

    Mung

    DNA_Jock, would you care to explain why it is that in the case of the ten of hearts you chose to not return it to the deck, whereas in the case of the seven of spades you chose to return it to the deck?
    What motivated those decisions, other than your desire to consciously manipulate the probabilities?
    If humans consciously and intentionally manipulate the probabilities, then the probabilities will change.

    DNA_Jock offers up scenario 2

    I was motivated by my desire to describe a situation in which the probabilities have changed. If you feel I am “cheating”, here’s an alternative scenario: Before shuffling the first time, I show you two cards, a heart and a club. After asking the first time “What’s the probability?”, I remove a card at random, show it to you, then ask the second and third questions. In this situation, neither of us knows the first or second probabilities, but we both know that the probability has changed. You know whether the probability has increased or decreased.

    Mung changes his mind:

    ok, yes. I agree. If you have a deck of 52 cards and you add 10 more cards to the deck, all of which are spades, the probability of drawing a heart will decrease even if you didn’t know the probability of drawing a heart in the first place.
    [Emphasis added for lulz]

    I point out that Mung has changed his mind.
    I point out that there are a couple of subtleties, regarding the special cases P(heart)=0 and P(heart)=1.
    I also point out that the size of the deck doesn’t matter.
    Finally the penny drops, and Mung starts backtracking, flailing wildly. He seizes on the P(heart)=0 and P(heart)=1 special cases, and tries to make out that this was his objection all along.
    Now Mung has reverted to disagreeing with the original statement:

    One does not need to be able to estimate the probability of an event in order to be able to describe situations in which the probability has increased or decreased.

    Claiming that he wanted to edit my statement to something he could agree with, viz::

    One does not need to be able to estimate the probability of an event in order to be able to describe situations in which the probability has changed.

    Huh?
    This could not possibly have been his objection, since HIS scenario, 52 cards, add 10 spades, fails for the P(heart)=0 case — where the probability has not changed at all.
    It doesn’t matter, since both of my scenarios are careful to describe situations where the P(heart)=0 and P(heart)=1 special cases do NOT pertain, and all I need to do to prove the statement correct is to describe a situation. Which I did. Twice. (The first time, I edited my comment to add the bit about the seven of spades: “ET avoid weaseling” I noted… I can see into the effing future!)

    One does not need to be able to estimate the probability of an event in order to be able to describe situations in which the probability has increased or decreased.

    Is true, despite all Mung’s flailing.
    Cue Mung retreating to the idea that 0.000001 < P(heart) < 0.999999 is an “estimate” of P(heart).
    ROFL

  22. RumraketRumraket

    Mung could just admit that he made a mistake. We all do it. It wouldn’t lessen my opinion of him, on the contrary.

  23. MungMung

    DNA_Jock: This could not possibly have been his objection…

    It’s been my objection all along. I have repeatedly maintened the exact same stance on it throughout.

    For example, I wrote to Rumraket:

    Mung: I explained quite clearly what the problem was. Your argument depends on relative frequencies and proportionality. Yet you leave unsaid the relative and proportional to what.

    Are you admitting that all you meant to say all along was that you could describe situations in which the probability has changed?

    Because now it seems clear to me that you’re admitting that in order to say in which direction it had changed, you would need additional details or assumptions.

    And that’s what I have been arguing all along.

  24. MungMung

    DNA_Jock: Thanks to the bias in our sampling procedure, our estimates of the denominator are going to be rather vague, I agree. But here’s the weird thing – 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. The only way that your argument would make any sense, would be if you were arguing that the denominator could have changed by a greater factor than the numerator — but you have not supported that position. Instead you seem to have been focused on the purportedly incalculable nature of the denominator. That is not actually relevant to the direction in which the quotient is moving.
    This ground has been covered before, recently. 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.

    If all DNA_Jock meant by increased or decreased was “changed” then whoever though otherwise?

    If he meant that he could say specifically which direction it had changed, for example, that it had increased, well, that’s what I was disagreeing with.

  25. MungMung

    Rumraket: Mung could just admit that he made a mistake. We all do it. It wouldn’t lessen my opinion of him, on the contrary.

    I would be happy to. To which mistake that I made ought I offer my assent?

    Here’s what DNA_Jock wrote:

    in order to know that the probability has decreased, you would need to know that there was at least one heart in the deck. Conversely, if we added hearts to the deck, in order to know that the probability has increased, you would need to know that there was at least one non-heart in the deck.

    That’s been my objection all along to what he initially wrote. In order to know the direction of change you would have to know additional details.

  26. MungMung

    DNA_Jock: But here’s the weird thing – 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 I asked DNA Jock. What’s the denominator? Because, how does he know the numerator is increasing relative to the denominator other than just declaring it to be so?

    For you see, to know that it’s increasing you have to be able to say relative to what.

    So I asked Jock:

    Mung: So what do we need to know to decide whether a probability has increased or decreased.

    Note the specific focus on how do we tell which of the two it is. Did it increase, or did it decrease, and in order to be able to say which, don’t we need to know that which it it increased relative to or decreased relative to?

    Hopefully it is clear that the simple fact that a probability merely changed was never the issue.

  27. MungMung

    Mung: If you are going to claim that some probability has changed, you need to know what it is that you’re talking about that has allegedly changed. Else you won’t know by which direction it changed.

    Again, rather clearly, the focus is on the direction of change.

    Did Jock ever say the direction is irrelevant because the only point he was trying to get across is that there would be a change? Because if so, I will gladly apologize to him for wasting his time.

  28. DNA_Jock

    Nope. The focus has always been on being able to detect the direction of the change.

    One does not need to be able to estimate the probability of an event in order to be able to describe situations in which the probability has increased or decreased.

    I even distinguished the two criteria in scenario 2.

    In this situation, neither of us knows the first or second probabilities, but we both know that the probability has changed. You know whether the probability has increased or decreased.

    I described a situation in which the probability has changed, in a direction known to you. I would know the direction of change IFF I saw the removed card too.
    But thank you for flailing.

  29. MungMung

    DNA_Jock,

    I never denied that it was possible to know the direction of change. I never denied that if you are possession of the relevant information you could know the direction of change. You’ve obviously misinterpreted my objections.

    Try again.

  30. DNA_Jock

    “I never denied that it was possible to know the direction of change.”

    One does not need to be able to estimate the probability of an event in order to be able to describe situations in which the probability has increased or decreased.

    Mung

    I disagree. If you are going to claim that some probability has changed, you need to know what it is that you’re talking about that has allegedly changed. Else you won’t know by which direction it changed.

    Suuuure.

  31. MungMung

    DNA_Jock: The focus has always been on being able to detect the direction of the change.

    Thanks for clearing that up. It means that I was in fact focusing on what was relevant, which is how you could know the direction of change.

    You can’t just take out a sample and declare the probability has changed. For example, removing a heart doesn’t tell you that the probability that the next draw will produce a heart has changed. Because perhaps they are all hearts.

    I’m still trying to ascertain what you think I was wrong about.

  32. MungMung

    DNA_Jock: Suuuure.

    Huh? That statement doesn’t deny that you can know. It points out that you need to know something else. Which we both agree on.

  33. DNA_Jock

    DNA_Jock: One does not need to be able to estimate the probability of an event in order to be able to describe situations in which the probability has increased or decreased.

    Is true, despite all Mung’s flailing.
    Cue Mung retreating to the idea that 0.000001 < P(heart) < 0.999999 is an “estimate” of P(heart).
    ROFL

    I can predict the future!

  34. MungMung

    I present you with a well shuffled deck of cards and ask you the probability of drawing a heart. You honestly answer that you do not know.

    Next, I remove a card from the deck, and show it to you — it’s the ten of hearts — and burn it. I also show you the seven of spades, and then replace the deck with a new one.
    Now I ask you two more questions:
    1) “What’s the probability that you draw a heart from this deck?”
    2) “Has the probability decreased since I first asked you?”

    What’s the difference between this scenario and the one offered by DNA_Jock.

  35. MungMung

    DNA_Jock: I can predict the future!

    It would be better if you could show:
    1.) Where I was wrong.
    2.) Where I claimed that we cannot know the direction of change.

    Do not know, and cannot know, carry two clearly different meanings.

    My statement stands:

    I never denied that it was possible to know the direction of change.

    ETA: To put it another way, I never claimed that it was impossible to know the direction of change.

  36. MungMung

    Still trying to make sense of what DNA_Jock is saying.

    So in the first case, the strategy was to change the composition of the deck in order to manipulate the probabilities. The deck had to be manipulated in a manner which would allow is to know how the probabilities changed.

    Where we had no knowledge of the composition of the deck relative to the number of hearts in it, now we do. That seems to be the message he’s trying to send.

    I agree that we don’t need to calculate the number of hearts in the deck nor even really estimate the number of hearts in the deck to know that we have changed the probability in such a way that it decreases the probability of drawing a heart (however slight that decrease may be), assuming that there are in fact hearts remaining in the deck. If there are no hearts left in the deck, then adding a spade changes nothing.

    Do we know whether or not there are any hearts left in the deck? If we do not know that hearts remain in the deck, can we say we know that the probability of drawing a heart has decreased? What would an honest person say?

  37. MungMung

    Mung: ok, yes. I agree. If you have a deck of 52 cards and you add 10 more cards to the deck, all of which are spades, the probability of drawing a heart will decrease even if you didn’t know the probability of drawing a heart in the first place.

    I was wrong, Rumraket. I assumed there were hearts still in the deck. If there are no hearts left in the deck then adding 10 spades doesn’t change anything.

    Bookmark this. 🙂

  38. MungMung

    DNA_Jock: Now, if you are being honest, your answers will be “I don’t know” and “Yes, the probability has gone down”

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

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

    So you see, I can be honestly mistaken. But you can also be honestly mistaken. I can admit I made a mistake. Can you admit you made a mistake?

  39. MungMung

    DNA_Jock: That [the denominator] is not actually relevant to the direction in which the quotient is moving.

    Assume the denominator is constant. Then to say that the quotient is moving is to say that it is moving relative to something other than the denominator. My questions have to do with that “something other.”

    If it’s not the denominator, what is it?

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