Response to the Criticism of “God Plays Dice”
ynet – 2011
Recently I came across a critique of the Rabbi’s article on “God Plays Dice” on YNET.
What does the Rabbi argue in response to the criticism?
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Rabbi:
Greetings.
Gadi Alexandrovitz is a very intelligent person, and his blog is truly fascinating. This article, to the best of my admittedly biased judgment, unfortunately fails, among other reasons because he did not understand my point since he had not read the book, and also because he decided to interpret the analogy too generously. One can always take nonsense that someone else said, convert it into a different argument, and explain that he uttered lofty wisdom. But what can one do—not that is what Gould said. And even if he did say it, he is mistaken, as I explained in the book (because the proof is outside the laws, whereas he makes a claim that is within the laws).
I wrote a detailed response to this post that appeared on a site founded by my student, but it disappeared from the web. Some of the responses published there appear on the site here, but I do not remember whether that includes a response to this post.
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Questioner (Gadi Alexandrovitz):
A few comments:
1) The critique is not of the book (which I had not read when I wrote the article; since then I have read it, and I do not think there is any additional interesting mathematical content in the book, so there will be no posts about it). The critique, as stated in the post, is of a specific article that the Rabbi published on the Ynet site and that is based on an excerpt from the book. Nonsense is written in that excerpt. Perhaps one can take the nonsense written in the article, convert it into a different argument, and explain that it contains lofty wisdom, but the text written in the article is nonsense.
2) There is no special attempt in my article to interpret Gould. There is not enough text in the excerpt the Rabbi published for one to identify what Gould’s argument was (I would be happy to receive a precise reference in order to see whether my guess was correct). As I note there, if my guess is correct then Gould’s argument is highly problematic, not “lofty wisdom” (in fact, I suspect that Gould did write something intelligent, and the Rabbi does him an injustice with the passing half-reference he gives).
3) It is a pity that the Rabbi did not also write the detailed response to the post as a comment on my post, in which case it would not have been lost.
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Rabbi:
Hello Gadi.
First, thank you for engaging. Since I was asked, and now I have again been challenged, I cannot help but write something more detailed. Especially since on the Ninth of Av (Tisha B’Av) one does not study Torah, so I have a golden opportunity to occupy myself with these matters, and perhaps thereby contribute something to redemption and to the rebuilding of the Temple (the vegetarian one, as I hope).
Since I saw that people I regard as very intelligent did not properly understand my point, I thought that perhaps I need to spell it out more fully. I therefore ask forgiveness for the length (as the venerable Mark Twain said: forgive the length; I did not have time to write briefly).
Clarifying my remarks on the importance of context
I will begin by saying that the subtitle of the excerpt on Ynet that you criticized (which was entirely supplied by the editors and not by me, and I share your criticism of the link they made there to Einstein) makes it abundantly clear that this is an excerpt from a book meant to give a taste of its contents, not an article (you yourself mention this, so apparently you did not miss it). It strikes me as somewhat odd that you treat it as an article that is supposed to make arguments and be self contained, and criticize it without knowing and understanding the background and context in which the remarks were made. That is what I meant when I wrote that you had not read the book and therefore your critique fails. But as I shall now try to show, it also fails on its own terms (that is, even without recourse to the context and the book as a whole).
A methodological note: the principle of charity
As I wrote in my short response on the site here, as part of your defense of Gould you “translate” Gould’s analogy and substitute another one in its place, and then criticize me for misunderstanding the analogy and evolution. This methodology is highly problematic on its face. Before I go into detail, let me preface my remarks with a methodological comment on your mode of argument.
Donald Davidson (a well-known American analytic philosopher) once formulated what he called “the principle of charity,” according to which one ought to interpret the person one is criticizing in the way most favorable to him and only then argue—and that is what you did. But I would add two qualifications to this pleasant principle: 1. The charitable interpretation should remain reasonably faithful to the source (that is, there should be a reasonable basis for assuming that this is indeed what the author meant). It is not reasonable to propose an interpretation that completely changes the original meaning (otherwise criticism and argument become impossible, since every failed argument in the criticized text will be replaced by a brilliant argument invented by the critic, and Zion is redeemed). 2. If you do this for Gould—namely, replace his argument with another one that withstands the criticism—why did you not choose to do the same for me?! For example, to conclude that although Gould probably meant your analogy, I probably understood him in accordance with what I wrote and therefore criticized him justly.
Moreover, even if you suspect that Gould meant something else, or even explicitly said something else and I did not understand him correctly, you may well be right (since I too rely on a secondary source. I did not see in Dawkins a reference to Gould’s original source), but in that case what you should do is simply say so: Abraham’s criticism is correct, but it does not seem likely to me that this is what Gould wrote. Perhaps he meant such-and-such, and then Abraham’s critical arguments fall away. But I do not see how you allow yourself to put into Gould’s mouth something entirely different from what I cited from him without knowing that this is what he said, and then to claim (albeit gently) that I understand nothing about evolution or any other field.
Lest you say: but is this not an application of the principle of charity?! Your interpretation is charitable toward Gould, as Davidson commanded. After all, you can assume (certainly if you are operating by the principle of charity) that I too know that the evolutionary tree is not composed of only one path, such that when it dies the process is over. I too know that there are masses of attempts and many drunkards who set out on the road. But what can I do—that is not Gould’s claim, and therefore I did not address that aspect either. Even stupidity has its limits, even that of a primitive believer like me. And even if it is possible that I am a complete fool (after all, we do not know each other), do I not deserve the protection of the principle of charity as well? Is Davidsonian charity extended only toward atheists and not toward believers? (True, that way at least there is no doubt the argument will end with the correct conclusion.)
The meaning of the drunkard analogy: between outcomes known in advance and outcomes dictated in advance
Unfortunately, at the moment I do not remember the source of Gould’s analogy. As best I recall, Dawkins cites it in one of his books (I will try to look again. It was a long time ago already). In any case, as I wrote, its purpose is to show that there are processes that appear random, and yet their result is dictated in advance because of external factors (circumstances) that hasten/accelerate them. Dawkins uses this in order to attack the assumption of the physico-theological argument for the existence of God. Admittedly, this seems a foolish argument, and as I shall show immediately it boomerangs against atheism, but it recurs quite often in atheist scripture, and in my opinion it actually illustrates the core of the physico-theological argument quite well, and that is why I chose this specific excerpt to pick on.
You “translated” this example into a random walk, what you called the gambler’s ruin phenomenon, which has an outcome known in advance (not dictated in advance). As a physicist, I prefer to look at it as a random walk rather than repeated gambling, although of course it is the same thing. Suppose there is a lattice, that is, a discrete collection of points at equal distances from one another along the x-axis (for the sake of simplicity, let us say the integer points on the axis). Some drunkard starts from some point on the axis, say x=n (what you called the initial conditions), and at every point where he is located he has probability p of swaying to the right and q of swaying to the left (the process is Markovian, that is, without memory, and let us assume the probabilities are constant at all points and times). The known result that you proved is that regardless of where he starts, he will eventually cross the origin (x=0) at some point in time (if I recall correctly—I am already a bit rusty—at least when p=q the time is proportional to n^2).
Your process is completely random, but its own properties (rather than external constraints) generate a dynamic with an outcome known in advance. Precisely for that reason it does not resemble the drunkard analogy in any sense, because that analogy deals with the influence of constraints and accelerants, and therefore your translation, though charitable to Gould, is irrelevant to the discussion. You propose another analogy in place of his, one that illustrates a different phenomenon, then analyze your analogy, and finally criticize my remarks, which dealt with his analogy. It seems to me that no one could blame me if I say that this methodology strikes me as problematic.
Incidentally, it should be noted that even in your translation the result (that at least one drunkard will reach x=0) does not follow from the data unless enough time passes (n^2) and/or enough drunkards set out on the road. To see in such a model an alternative to the existence of an intelligent factor, one must show that these conditions are in fact met (that there are enough drunkards and/or that enough time has passed). I note that various calculations claim that they are not met (with respect to abiogenesis, even Dawkins argues in favor of the thesis of a “lucky accident,” and de-Rob and many others reject this on the basis of a calculation of the number of attempts and the time scales. See also the notes at the end), but that is not our topic.
Let me add a further clarification regarding the claim that emerges from the drunkard analogy. When I looked for the source of these remarks (and unfortunately did not find it; I do not have all of Dawkins’s books at home), I found in The Blind Watchmaker, p. 61 and onward, a very similar analogy, in which Dawkins refers to the formation of a meaningful sentence by a random process of keyboard strikes (as a monkey dances on it). Let us say we want to generate the Hebrew equivalent of the sentence “Methinks it is like a weasel” (in the original experiment that I discussed in the Ynet article, the sentence was: “tobeornottobe”) by random strikes on the keyboard. Of course, this involves a program with a random character generator and not an actual jumping monkey. There are 21 characters here, and if we assume that in Hebrew there are 27 letters (including the final forms) plus a space, then there are 28 possibilities for each keystroke, and the probability of obtaining the entire sentence is 28^(-21). That is something like 1 divided by a number with thirty zeros, that is, truly negligible. Therefore the time it would take to reach the “correct” combination is enormous (depending, of course, on the rate of typing, drawing, or monkey-jumping). That is with respect to a one-step random draw. But what will happen in the process he calls there “cumulative selection”? This is a process in which the string produces many “offspring,” from among which we choose the one that most resembles the desired string (!), no matter how slight the resemblance may be. [I did not see there a specification of how many offspring are produced at each step.] Surprisingly, Dawkins reports to us, in such an experiment one reaches the goal after a few dozen “generations” (by the 50th or 70th generation). As best I recall, in the computerized “tobeornottobe” experiment they did something slightly different: every time they obtained a correct character in the correct place in the string, they froze it and randomized only all the rest. And lo and behold, there too the process was dramatically shortened.
Dawkins’s conclusion (p. 65 there): There is therefore a great difference between cumulative selection (in which every improvement, however slight, serves as a basis for future construction) and single-step selection (in which every new “attempt” begins from zero). If evolutionary progress had had to rely on single-step selection, it would never have gotten anywhere. But if there is some way in which nature’s blind forces could establish the conditions necessary for cumulative selection, then the results would be strange and wonderful. In fact, this is exactly what happened in our world, and we ourselves are among the most recent—if not the strangest or most wondrous—of those results.
That is, he is talking about a non-Markovian process (one that has memory. Every step in the randomization remembers previous results and depends on them). In fact, it not only remembers the past, it also knows the future (what the goal is, since within the process it repeatedly compares itself to it). This is in complete contrast to the random-walk analogy you presented.
Note that in his analogy he is speaking about a result dictated by external constraints, not a random result known in advance (as in your random walk). His claim is that evolution is not merely a collection of random (Markovian) draws, but draws under external constraints that remember what has happened and know where things are headed, and thus dictate the outcome and accelerate its arrival. There is an external factor here—if you like, the programmer—whose intervention alone brings this “random walk” to the desired result. There you have our much-maligned drunkard analogy itself, in which the wall brings the random drunkard to the destination we desire. Is it also proper, with respect to Dawkins’s own words, to apply a charitable interpretation and change his analogy into something Markovian, without constraints and without memory?
My claim is that an analogy like that of the drunkard is extremely common in these discussions, and therefore it is not terribly important what exactly Gould said. From this it also follows that there is no basis for your assessment that he could not have said this, and still less for the generous “translation” you proposed for him. In any case, my remarks criticize the argument that deals with the effect of circumstances and constraints on a random walk, not an argument like yours that deals with probabilistic outcomes of a random walk that are known in advance. As far as I am concerned, this is a criticism of Dawkins and not of Gould (see also the notes at the end).
The conclusions from a process whose outcomes are dictated in advance
So we have returned to discussing an analogy whose outcomes are dictated in advance by external constraints (and not merely known in advance, as in a random walk). I doubt it is necessary to explain to readers, and certainly not to you, the theological significance of Dawkins’s example. What he is demonstrating is that although the evolutionary process is not probabilistically feasible, if we add a guiding hand (teleological, that is, result-oriented, in a rather blatant way)—namely, a programmer who ensures that the randomization in the computer reaches the destination we desire—it becomes something feasible. Does that remind one of the drunkard analogy? Certainly yes. The drunkard too cannot, by a random walk, reach any given goal, but if one creates circumstances around him (a gutter and a wall) that ensure that he arrives—he indeed will arrive. And in the analogue, a random draw of a “successful” protein chain is not plausible, but when one breaks it down into cumulative stages, that is, when there are “external” factors that direct it all along the way (natural selection, heredity, etc.), it becomes plausible.
These analogies are used by Dawkins when he comes to refute the physico-theological argument, but in fact this is precisely the physico-theological argument: it claims that in order for an improbable process to succeed, a guiding hand is required, and these analogies only strengthen that argument rather than refute it. And in the analogue, in order for the evolutionary process to take place with a reasonable probability, there must be a guiding hand that sets the rules of the game so that the result will be obtained. With other rules of the game, or without rules of the game at all, this probably would not happen. The physico-theological argument claims that this guiding hand is God (for the purposes of the discussion, one may say that this is really His definition rather than a claim about Him).
Notice that the analogies of Dawkins and Gould do not rely on there being many repeated attempts, as you put into his mouth. They are about the influence of a guiding hand, laws, or circumstances that affect the process from the outside. The focus of the discussion is: what are these external “circumstances”? Who created them? The neo-Darwinians claim that these are the laws of nature (which cause the formation of random mutations and the genetic inheritance of their traits, and in fact the entire evolutionary process, and thereby direct it toward its goal and render the assumption of an intelligent factor unnecessary). The random walk takes place within them and under their influence, and therefore it can reach its goal. This is the scientific explanation, and I accept it completely. But my question is on the theological-philosophical, extra-scientific plane: where did these very special laws come from, without which none of this would have happened? There is a guiding hand here that leads the drunkard (by means of the wall and the gutter) to his goal. Had there been no wall and gutter there (in Gould), and had there been no comparison of the string to the desired string (in Dawkins), the desired result would not have been achieved. As we have seen, Gould and Dawkins themselves inserted external elements into the system with their own hands so that randomness would lead to the desired result. In Dawkins this is even more blatant, for he inserts the desired result itself into the process (by means of comparison at each stage to the desired string). That is already a real “own goal,” because he describes evolution as something goal-directed that was designed in advance to arrive there. He puts God inside and then claims that He is no longer needed. [Like that dear Jew who cannot find parking and turns to God in fervent prayer to help him. In his distress he promises Him that from now on he will dedicate his life only to Torah and commandments. And behold, right beside him a parking space opens up. Our friend is not confused, and immediately turns back to God: “No need, thank you, I’ve already managed on my own.”]
Let us now return to the analogue. Evolution is a description of a process that takes place within the laws (=the wall and the gutter), and they are what ensure that it “succeeds.” Without them this would not happen. I now ask about the laws themselves: where did they come from? The physico-theological argument concludes that it is plausible that there is a guiding hand that leads the evolutionary process to its goal. So what is surprising about the fact that it indeed gets there? These analogies are not a refutation of this argument, but rather an excellent illustration of the thesis that an external intelligent factor is required to lead the process to its goal (to moderate the slope of the improbable mountain).
If you insist on saying that the laws came into being on their own or that they always existed and their character was determined arbitrarily, that is perfectly fine by me. In that case the physico-theological argument truly will not persuade you (every logical argument addresses only those who accept its premises). But notice that you are assuming from the outset that a special thing (=the laws) can come into being blindly. If so, what has all the evolutionary casuistry added for us? If you assume that special phenomena do not require a guiding hand, then of course you do not accept the physico-theological argument (that complex phenomena testify to the existence of an intelligent guiding factor). And if you assume that this is implausible, then you do accept it. Either way, evolution is irrelevant to the discussion, and the arguments about drunkards or monkeys and keyboards are even less relevant.
A few concluding remarks
A. Of course the discussion is not over. One can now discuss whether life is indeed “special” in some sense, or whether we marked the target after it was created. One can also discuss whether the laws are special. Dawkins deals with this later in The Blind Watchmaker, and in my opinion he is mistaken there as well, and badly so. One can further discuss whether the thesis of an intelligent factor solves the problem, and whether the term has any meaning at all. I dealt with some of these matters in my series of articles on Ynet. But all this already goes beyond the discussion of the passage at hand. Here I wanted to explain what I meant in this specific passage and clarify why your criticism does not address my remarks. For the continuation of the discussion I can only refer the reader to my articles on Ynet and to reading the book.
B. As far as I know, Gould too is an atheist, but he disagrees with Dawkins in a serious dispute (sometimes very stormy) regarding the status of God from the standpoint of evolution. Dawkins claims that evolution proves (almost with certainty) that He does not exist, whereas Gould thinks the questions are independent of one another (perhaps evolution renders the claim of His existence unnecessary, but does not prove anything about Him). I too think the questions are independent, because as I showed above the debate depends on the point of departure (whether a complex thing can come into being/exist without an intelligent guiding factor), and evolution neither adds nor subtracts anything in this regard. I explained this above. What I added regarding the strengthening of the physico-theological proof is that if the point of departure is that it is implausible for a complex thing to exist without an intelligent factor that creates it (this is what that argument assumes), then evolution strengthens the physico-theological argument. Of course, one who disputes that assumption will not accept the conclusion, with or without evolution, and that is perfectly fine at least from the standpoint of logical validity (although to my mind the assumption is a bit irrational). Therefore evolution in any case is not connected to the discussion. These matters are clarified more fully in the book itself. My disagreement is mainly with Dawkins, and as far as I am concerned the analogy Gould brought is not important (although it is imprecise). What concerns me here is chiefly the use Dawkins makes of it to attack the thesis of God’s existence.
C. Of course this entire discussion deals with one drunkard, and as you quite rightly noted, in the evolutionary process there are many drunkards. Notice that in Dawkins’s analogy about the desired string this has already been taken into account, since many randomizations are carried out there and not just one. But as I explained, even in the drunkard analogy this is not the effect under discussion, but the state that arises after we have already taken it into account. That is, his claim concerns a situation in which even if there are many drunkards, the probability that one of them will reach the gutter is still small—unless there is a wall that ensures it. Therefore the drunkard analogy ignores the number of drunkards, and therefore I ignored it as well (although I did add a brief discussion of a paper wall with rigid points that hints at this aspect).
Incidentally, my book contains a calculation by de-Rob that shows this also in the evolutionary context (actually in the context of abiogenesis—namely, that even if one takes into account the very large number of attempts that were made, the probability of the formation of a “successful” chain is negligible. He gives there a rough estimate of how many attempts were made), and the question is treated there broadly and in detail. So do not worry: I know very well that one does not do statistics on a single case, and I am sure that Gould and Dawkins know that as well.
D. Suppose now that this response were long (purely hypothetically, of course), and on Ynet they were to bring from it only the seventh paragraph, in order to illustrate what was at issue. Would it be appropriate to criticize what was said in that paragraph as though it were an article making a claim? That is essentially what you did in your post. But, as stated, my claim here is that your criticism does not hold water even on its own terms, that is, even without entering the whole book and the context. In my short response on the site I noted that the problem is both that you had not read the book and also considerations that pertain to this excerpt itself (the confusion between a discussion outside the laws and a discussion within the laws, and an overly generous interpretation of the analogy).
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Questioner (Gadi Alexandrovitz):
With your permission, I think it is better to focus the discussion. My experience is that extremely long responses spill far beyond the scope of the discussion, and there is no reasonable way to address them.
So to the point itself: I am surprised to discover that you presented an argument you attribute to Gould and attacked it without actually having read the argument or even having a reference to it. That is not really appropriate, because then it is not at all certain that you understood what Gould was trying to say by means of the analogy (if anything).
In my post I say: “Gould (of this I am completely certain) thinks of the drunkard at the very least as a population of some species.”
Here are a few focused questions. A focused and brief answer to them will help the discussion.
1) Are you claiming that this is not the case?
2) Are you claiming that Gould is thinking of the drunkard as a single organism?
3) In your text, how do you understand the drunkard analogy? To what does the drunkard correspond for you? A single organism? A population? The entire process? What is the meaning of the gutter, and what is the meaning of the “paper wall” in your account?
4) You say, “in the evolutionary process we do not have a wall that ensures that each time the drunkard returns anew to the path.” Why is this important? As I explain in the post, the wall is entirely meaningless. Mathematically, the behavior of the drunkard-with-a-wall and drunkard-without-a-wall models is similar: with a 50:50 probability the drunkard will ultimately fall into the gutter (whether there is or is not a wall), and if there is a bias in favor of walking away from the gutter, it is not guaranteed that the drunkard will ultimately fall into the gutter (whether there is or is not a wall).
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Rabbi:
Hello Gadi. With your permission, I shall skip the rebukes and the counter-rebukes.
A. I completely agree that Gould is speaking about a population. That is precisely what I wrote (that for the purposes of the discussion one may say that the effect of multiple drunkards is included in the model).
B. You are entering into unnecessary hairsplitting. The analogy is meant to say that sometimes external constraints accelerate the random process and focus it (moderating the slope of the improbable mountain, in Dawkins’s formulation). That is also what emerges from Dawkins’s analogy of the jumping monkeys.
C. The rest of your remarks concern your model, and as I explained it is irrelevant to the discussion, and not for nothing do neither Dawkins nor Gould (apparently), nor even humble me, deal with it. I must say that by doing so you are repeating the same methodological distortion about which I elaborated in my remarks (apparently it would after all have been worthwhile for you to read them), and therefore I will not enter into a discussion of that.
D. In my analogy it is clear that there is a difference between the model without the wall and with the wall. It seems to me that simple probability calculations would be agreed upon by both of us, and there is no point getting into riddles about them.
E. I will now explain again why your model is not relevant to the discussion. A random walk as you described it (without constraints) is an empty mathematical model. It contains no component connected to laws of nature (=external constraints), and its result is known in advance solely from probability calculations (and does not really depend on the values of the parameters, as you quite rightly showed). It follows that there is no representation there of the influence of any laws of nature. If one assumes that your model models evolution, it follows that evolution is a branch of mathematics and not of empirical science, and that is of course nonsense. I assume we would agree that in a world with different laws of nature none of this would happen.
Therefore the drunkard model similar to what I described (and it really does not matter to me if you change this or that detail in it), as well as the jumping-monkeys model (Dawkins), are indeed the correct models for evolution (apart from corrections I pointed out in my remarks, but clearly we are not talking about stripping away the environmental constraints, as you suggest). The external constraints in these models (the wall and the programmer), which do affect the outcome, and necessarily so, express the influence of the laws of nature within which the random process takes place.
Except that, as I argued, precisely for that reason these models clearly illustrate why the evolutionary picture does not exempt us from the conclusion that there is a guiding hand (unless one accepts that complexity can arise on its own, in which case again evolution is irrelevant to the discussion).
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Questioner (Gadi Alexandrovitz):
Let us focus further.
If you agree that “Gould is speaking about a population,” I want to understand, before the discussion can continue, why you wrote: “the main problem is that the wall along which the drunkard advances is made of paper. Moreover, behind this wall there is an abyss from which none return. Any movement in the direction of what is evolutionarily non-viable (that is, toward the wall) leads to a dead end of the process, that is, to the extinction of the creature or of its evolutionary descendants.”
1) “the extinction of the creature” — what creature is being spoken of, if we are talking about an entire population?
2) If you are indeed thinking of an entire population, what is the paper-wall analogy meant to represent? Is it meant to describe an evolutionary change that causes the extinction of an entire population?
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Rabbi:
Indeed. If one does not take into account the “external accelerators” (=the wall), the fate of the entire population (=the gene pool) is extinction. A dead end in the evolutionary process does not speak of a single creature but of a population or type (=the gene pool). Evolutionary development wipes out most creatures and leaves the strong ones (the survivors). But even the survivors survive only thanks to the wall (=the laws of nature), and were it not for it they would all reach a dead end. Exactly as Dawkins explains that the slope of the mountain is improbable (before the moderation). He does not mean a single creature climbing the mountain but the gene pool.
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Questioner (Gadi Alexandrovitz):
You are contradicting yourself.
In your article you wrote about a “wall made of paper.”
What is the wall? Why is it made of paper? Give concrete examples from the world of evolution. You later say, “we will add to our model the fact that there are a tiny number of points on the wall that are made of hard stone, and striking them will send the drunkard back to the sidewalk.” Can you give real-world examples of such an evolutionary wall?
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Rabbi:
As far as I know, a contradiction is always between two things. I wrote that the wall is made of paper. So? Where is the second horn of the dilemma? As for your remarks: first, on the level of the genotype. If you look at the set of all protein chains, there are masses of them (an ocean). Of them, only an utterly negligible number are genetic structures that have a “living” phenotype. These are small islands in a “dead” ocean. Evolution is basically a random walk among them, that is, hopping between these islands. The jump has to take us from one living island to another living island. Missing such a jump is a dead end. Because these islands are so rare, this would never happen in an ordinary random walk (without constraints) were there not laws of nature here (a wall) that ensure that it does happen, that is, that there be a reasonable number (it may still be tiny, but enough for the gene pool to survive) of jumps in the ocean from the island where one is located to other “living” islands. These laws turn the wall from a paper wall (with a few rigid points) into a solid wall, or alternatively ensure that a sufficient number of jumps strike its rigid points. And here is an example on the phenotypic level. Consider the case of Darwin’s finches. There was a drought on the island and all their food plants died out. Only plants remained whose cracking required a particularly strong beak, and thus the finches with strong beaks survived and passed that trait on to their offspring. It could have been that all the plants would die out, or that there would be no birds with strong beaks, because the finch’s mutations might have produced a crippled elephant or just some structure whose phenotype is not a living creature (a three-winged fairy). Alternatively, if there were no laws of heredity, then even though that trait was selected in the natural process it would not pass to the offspring, and the finches would become extinct. The laws of evolution (the formation of mutations + selection + genetics) moderate the slope of the improbable mountain and ensure that the mutations also produce something close, such as a finch with a strong beak, and/or that not all the plants always die out. Thus the finches’ gene pool survives and passes to the next generation. If what we had here were merely a random walk (without the accelerating influence of the laws of nature), it is not plausible that this could happen.
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Questioner (Gadi Alexandrovitz):
I understand (I do not agree, but at least I understand).
Your claim is that Gould claimed this was a completely random walk? Prove it.
Well, I decided that it would be better if I did the research that has not been done here so far. Gould’s use of the analogy is taken from his book “Full House: The Spread of Excellence from Plato to Darwin.” I will bring the relevant part in full. TL;DR: as I thought, Gould is not trying in any way to claim that the drunkard analogy describes evolution at all. He brings it as a simple mathematical example of the way in which, in a random process (one in which there is a 50:50 probability in each direction), a preference is created for a certain direction (the gutter).
I think he is mistaken in his interpretation. He brings in the wall as the reason the preference is created. To the best of my understanding, the wall has nothing to do with it and could have been dispensed with entirely; the reason a “preference” is created is that once one reaches the gutter—that is it, one is stuck there. If there were no gutter, the process would reach arbitrarily great distances on both sides and that would be the end of it. In other words, I think Gould is using an incorrect mathematical metaphor here, although with a more careful mathematical analysis of the drunkard-with-a-wall situation one might perhaps obtain something that matches what he wanted to say.
If so, what was done in the Ynet article is of course not fair. The article attacks the analogy as though the analogy were meant to describe evolution. According to Gould, explicitly, the analogy is not meant to do that but rather to clarify a more basic point.
(I personally think that any attempt to describe evolution by means of this analogy is utterly ridiculous, which explains the foolish discussion that is taking place here as well).
“In the case of 0.400 hitting. I spoke of a limit or ‘right wall’ of human biomechanical possibility, and I illustrated the decrease in variation of batting averages as the full house of hitters moved toward this upper bound. In this section on complexity in the history of life, I shall present something close to a ‘mirror image’ case—an increase in total variation by expansion away from a lower limit, or ‘left wall,’ of simplest conceivable form. The cases may seem quite different at first: improvement in baseball as decrease in variation by scrunching up against a right wall of maximal achievement versus increase of variation by spread away from a left wall of minimal complexity, misconstrued as an inevitable, overall march to progress in the history of life. But a vital and deeper similarity unites the two examples—for both represent the same mode of correction for the same kind of error. In both cases, the error involves false portrayal of a complete system of variation by a single ‘thing’ or entity construed as either the average or the best example within the system. Thus we tried to map the changing status of batting through time by tracing the history of the best conceived as a separable entity (0.400 hitters). Since this ‘thing’ disappeared through time, we naturally assumed that the entire phenomenon—hitting in general—had gotten worse in some way. But proper consideration of the full house—the bell curve of batting averages for all regular players—shows that 0.400 hitting (properly viewed as the right tail of this bell curve, and not as a separable ‘thing’) disappeared because variation decreased around a constant mean batting average. I then argued that we must interpret this shrinkage of variation as an indication of general improvement in play through time. In other words, by falsely isolating 0.400 hitting as a thing to be traced by itself, we got the whole story entirely backwards. The partial tale of the ‘thing’ alone seemed to indicate degeneration of hitting; proper consideration of changes in the full variation showed that disappearance of 0.400 hitting represents improvement in general play. We have traditionally made the same error—and must now make the same correction— in studying apparent trends to increasing complexity, or progress in the history of life. Again, we have abstracted the full and rich complexity of life’s variation as a ‘thing’—by taking either some measure of average complexity in a lineage or, more often, the particular case judged ‘best’ (the most complex, the brainiest)—and we have then traced the history of this ‘thing’ through time. Since our chosen ‘thing’ has increased in complexity through rime (once bacteria, then trilobites, now people), how could we possibly deny that progress marks the definition and central driving principle of evolution? But I shall try to make the same correction in this part by arguing that we must consider the history of life’s complexity as a pattern of change for the full system of variation through time. Under this properly expanded view, we cannot regard progress as a central thrust and defining trend—for life began with a bacterial mode next to the left wall of minimal complexity; and now, nearly 4 billion years later, life retains the same mode in the same position. The most complex creature may increase in elaboration through time, but this tiny right tail of the full house scarcely qualifies as an essential definition for life as a whole. We cannot confuse a dribble at one end with the richness of an entirety—much as we may cherish this end by virtue of our own peculiar residence. Before presenting the full argument for all of life, I must first explain why a dribble moving in one direction need not represent the directed thrust of causality within a system—but may actually arise as a consequence of entirely random movement among all items within the system. I will then demonstrate, in the next section, that apparent progress in the history of life arises by exactly the same artifact—and that, probably, no average tendency to progress in individual lineages exists at all. I shall first illustrate the argument as an abstraction—using a classic pedagogical metaphor beloved by teachers of probability. Then I shall provide an intriguing actual case for a lineage of fossils with unusually-good and complete data. Since we live in a fractal world of ‘self-similarity,’ where local and limited cases may have the same structure as examples at largest scale, I shall then argue that this particular case for the smallest of all fossils—single- celled creatures of the oceanic plankton—presents a structure and explanation identical with an appropriate account for the entire history of life. Since we can approach these largely unknown plankters without the strong biases that becloud our consideration of life’s full history, we can best move to the totality by grasping this self-similar example of oceanic unicells. The overall directionality in certain kinds of random motion—an apparent paradox to many—can best be illustrated by a paradigm known as the ‘drunkard’s walk.’ A man staggers out of a bar dead drunk. He stands on the sidewalk in front of the bar, with the wall of the bar on one side and the gutter on the other. If he reaches the gutter, he falls down into a stupor and the sequence ends. Let’s say that the sidewalk is thirty feet wide, and that our drunkard is staggering at random with an average of five feet in either direction for each stagger (See Figure 21 for an illustration of this paradigm); for simplicity’s sake—since this is an abstract model and not the real world—we will say that the drunkard staggers in a single line only, either toward the wall or toward the gutter. He does not move at right angles along the sidewalk parallel to the wall and gutter. Where will the drunkard end up if we let him stagger long enough and entirely at random? He will finish in the gutter—absolutely every time, and for the following reason: Each stagger goes in either direction with 50 percent probability. The bar wall at one side is a ‘reflecting boundary.’[8] If the drunkard hits the wall, he just stays there until a subsequent stagger propels him in the other direction. In other words, only one direction of movement remains open for continuous advance—toward the gutter. We can even calculate the average amount of time required to reach the gutter. (Many readers will have recognized this paradigm as just another way of illustrating a preferred result in coin tossing. Falling into the gutter on one unreversed trajectory, after beginning at the wall, has the same probability as flipping six heads in a row [one chance in sixty-four]—five feet with each stagger, to reach the gutter in thirty feet. Start in any other position, and probabilities change accordingly. For example, once the drunkard stands in the middle, fifteen feet from the wall, then three staggers in the same direction lone chance in eight for a single trajectory! put him into the gutter. Each stagger is independent of all others, so previous histories don’t count, and you need to know only the initial position to make the calculation.) [8. In more complex cases involving several entities, the wall might be an ‘absorbing boundary’ that destroys any object hitting it. No matter I so long as enough entities are left to play the game—certainly the case, with lift’s history). The important point is that an entity can’t penetrate the wall and continue to move in the wallward direction—whether or not the entity bounces off or gets killed.] I bring up this old example to illustrate but one salient point: In a system of linear motion structurally constrained by a wall at one end, random movement, with no preferred directionality whatever, will inevitably propel the average position away from a starting point at the wall. The drunkard falls into the gutter every time, but his motion includes no trend whatever toward this form of perdition. Similarly, some average or extreme measure of life might move in a particular direction even if no evolutionary advantage, and no inherent trend, favor that pathway. ”
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Rabbi:
Hello Gadi. We began with the claim that I understand nothing about evolution, nothing about mathematics, and in general I speak nonsense. I now get the impression that we are in a somewhat different situation. I shall try to explain again how I understand the matter. If you wish to continue the discussion (the foolish one, by your own definition as well, and with which I entirely agree), please tell me what exactly your original claim in your post was about. I would appreciate it if at this stage you would not raise new claims, but only explain what you meant when you said that I understand nothing and speak nonsense (within the framework of the excerpt published on Ynet). After that we can discuss other matters if you wish. 1. Background to my claim: evolution is essentially a kind of random process that, on a simple probabilistic calculation (=outside the laws), has almost no chance of being realized. The fact that it is in fact realized is explained by the fact that this random process occurs within a framework of external constraints (=within the laws. The laws of nature: biology—and within it physics and chemistry—genetics, modes of mutation formation, and more). In this way evolution is part of the natural sciences and not of mathematics. My basic claim in the book is that if there are external constraints and only because of them we have gotten this far by a blind and random walk, it is plausible to assume that there is an intelligent factor that created them and thereby in effect caused this result. As stated, this claim is not necessary, but it is highly plausible (in my view). Anyone willing to accept complex things without an intelligent factor will of course reject the conclusion. But every logical argument addresses those who adopt its premises (very plausible premises in this case, in my humble opinion). 2. That is the background, and now to the excerpt under discussion that was published on Ynet. I remind you—your remarks concerned only it (since the background was apparently not known to you at all): A. I brought there the drunkard analogy and argued that it comes to express the idea that a random process can reach its goal with the help of external accelerants/constraints. This is a claim Gould himself makes in the excerpt you brought, and Dawkins does so in countless places as well. Those accelerants are basically the aforesaid laws of nature. In my remarks to you on my site I added Dawkins’s analogy about the random creation of a string of characters, which says exactly the same thing on the level of principle. B. I then argued that these analogies do indeed correctly describe evolution (see the background in section 1), but the point is that they do not refute the physico-theological argument concerning God; rather, they illustrate its logic quite well (for those who accept its premises, as stated above). They show that in order for a random process to reach a complex result, a guiding hand is required. That is more or less what I wrote there. 3. Now to your post: you claimed, in general terms, that my remarks in that excerpt (that is, the final sections A-B above here; you did not know the background at all) reflect a mathematical misunderstanding, that I know nothing about evolution, and that I am speaking nonsense. That seems to me a fair, if somewhat concise, summary of what you said about me. In addition, you proposed another, somewhat fanciful explanation for Gould’s analogy, which you now also agree is not really what is written there. You also agree that Gould made exactly the mistake you attributed (mistakenly) to me, in saying that the wall affects the result. In the analogy as I understood it, it indeed does affect the result. 4. So what remains of all this? At the moment it seems that all that remains is for us to interpret Gould’s holy writ, and determine whether Gould stated the analogy exactly this way or another. That does not really touch the substance of my claims, and certainly does not point to any mathematical or scientific misunderstanding, as you attributed to me. Therefore it does not touch the main point of your post in any way. But if for some reason you still wish to know my opinion about Gould’s remarks—which, as stated, is really not important in my eyes—I still stand by everything I wrote about them. Gould does indeed describe the idea of evolution in this analogy (as he explicitly writes here), he shows through it that external constraints can focus a random process, and of course he also introduces the wall into it (which, according to you, has no effect). Therefore, in answer to your question in the last message in this thread, in my view he is not dealing with a random walk. I will now only add that if, as an atheist, he assumes that there is no guiding hand, then in my opinion his remarks are really not plausible. I can only agree that the discussion here seems somewhat pedantic and foolish, as you wrote, since from all the big ideas and sweeping accusations we have arrived at parsing that righteous man’s exact meaning (Gould). But it seems to me that this is not really my fault. 5. And one more reminder: I cannot help returning to the methodological problem I pointed out in my long response, and also to your claim about a contradiction between one statement of mine (that the wall is made of paper) and… to this moment I do not know what (which reminds me of the nonsense question “What is the difference between a rabbit?”, or the well-known Zen question: what sound does one hand clapping make?). 6. And in conclusion: now that you understand what I meant (even if you do not agree, and that is perfectly fine from my standpoint), I would be glad and appreciative if you saw fit to insert some correction or apology regarding the inflammatory and unfounded post, which is very unlike you. Precisely because I greatly value your writing, and apparently others do as well. Even if you do not see fit to do so—there is no problem at all. We can part as friends after our brief chavruta (study session) here. It was a pleasure to meet.
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Questioner (Gadi Alexandrovitz):
1. This background is clear. I think it is misleading to readers because one cannot define anything “outside the laws,” although I would be happy to see you define formally a random process for evolution that is outside the laws such that one can perform on it the kind of “simple probabilistic analysis” you describe. This background is not included in the article that appears on Ynet and therefore is not really relevant to the critique.
2.
A. That is not what Gould says, but let us leave that aside.
B. That is not what you do in the article. In the article you take the analogy, which Gould is not at all trying to claim describes evolution, and say that it is wrong (“the problematic nature of this analogy lies on two different levels…”, “Gould’s absurd model”
).
Here, in my view, you seriously mislead the reader. You take a toy model that no one claims describes evolution, disqualify it (and therefore Gould) as an incorrect description of evolution, and then use that same toy, with slight variations, to describe evolution. That is absurd. You are using a ridiculous and utterly simplistic model to speak about evolution.
I do not know whether you intended this, but the impression created is that you are trying to make the reader think that if Gould used this model to describe evolution, then it is acceptable to speak about evolution by means of this model, and only a few corrections are needed (for example, your wall made of paper). After all, Gould is one of the “good guys.” This is a serious misleading of readers, and I very much hope that was not what you intended; but if it was not what you intended, then it is beyond me why you are speaking about this model here in the first place. Gould brought it in order to make a very specific claim, one that you neither refute nor even discuss at all.
3. What I say is: “About this argument I can say either that I understand nothing about evolution, or that Rabbi Dr. Abraham understands nothing about evolution (or that neither of us understands anything about it).” That is, I am not really pretending to say anything about Rabbi Dr. Michael Abraham, whom I have not examined and whose education I do not know; I am saying something about the argument that appears in the quoted paragraphs.
I agree that the interpretation I proposed for Gould was fanciful, because at the time I mistakenly thought that Gould was indeed trying to use the drunkard analogy to describe evolution. I blame your article for that misleading impression. If you wish, I can correct my post so that it absolves Gould of the charge of attempting to use the drunkard analogy as an evolutionary model, and explain that what is involved is a misleading move performed by your article.
Now, I assume you want to say that the paragraphs I mock in my article are not as foolish as I present them. Perhaps. But for that you will have to explain precisely what they mean and how that meaning follows from the text; not propose other ideas that appear in your writings elsewhere and contradict your text. In the text it is written, for example, “in the evolutionary process we do not have a wall that ensures that each time the drunkard returns anew to the path.” In the texts you write here, suddenly there is a wall, and it is the laws of nature (which, of course, are engineered by God).
So I propose: do you want to rescue the article? Take the three paragraphs I quote, and write an explanation for them. The explanation should include: the precise mathematical model you are using to describe evolution; the aspects of evolution that correspond to the mathematical model; the meaning of every vague word in your text; and so on. Then we can discuss.
For example, what is an “evolutionary step”? Is it a single mutation that appears in a single individual from the group? If so, why does such a step, if it leads to the creation of a “non-living mutation,” stop the evolutionary process at the group level? (It does not.) If not, how common is it? Do those probabilities correspond to the probabilities in the mathematical drunkard model, in which the probability of walking toward the wall is identical to the probability of walking in the other direction? And so on and so forth.
4. As I have tried to say here several times, Gould does not really interest me, and my post is not really trying to defend him. Nevertheless, in my view the interesting part of the whole story is that it became clear to me here that you had not read Gould’s text at all before writing the article.
5. The contradiction is between describing the wall as something capable of sending back whoever strikes it, and describing the wall as made of paper, so that everyone who passes through it becomes extinct. Later in your article you change this model to a wall with “a tiny number of points on the wall that are made of hard stone,” and this resolves the contradiction (that is, it replaces the contradictory models with a unified model), but to see that I had to bother to reread the article.
This sharpens what bothers me in your writing: you begin, unnecessarily, with incorrect models, without even hinting that they are incorrect, and after prolonged engagement with them that is not actually useful for anything, you quickly move on to speak about the less incorrect models. Another problem is that even the less incorrect model does not necessarily correspond to reality, but we have already discussed that.
6. As I suggested in section 3, I am willing to correct in the post my attempt to guess what Gould meant, and to clarify that your article misled me into thinking that Gould was actually trying to provide an evolutionary model by means of the drunkard analogy, whereas in fact he was not.
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Rabbi:
Hello Gadi. Unfortunately, you are fleeing into foreign and irrelevant territories, and that is a pity. Things I have already explained thoroughly, you keep demanding to have explained again. You demand a calculation where no calculation at all is needed in order to understand the claim, and you send me off to write Rashi and Tosafot on my words and on Gould’s words, even though in your opinion they are mistaken (and in my opinion not), and even though you admitted that your understanding of them was also mistaken (although, in a peculiar rhetoric, I am the only one to blame for this). I repeat for the who-knows-how-manyth time that these models are not intended to describe evolution in its entirety but the idea of evolution, namely: that external constraints accelerate or improve the focusing of a random process and the probability of attaining a “successful” result. This is the main idea of evolution, and on that there is no dispute between me and Gould and Dawkins and anyone else who understands the matter. Almost all of Dawkins’s books, as well as part of Gould’s writings, are devoted to this, and the model illustrates it quite well. For my purposes that is entirely sufficient. 1. Of course one can, and it is even very easy, and I have already done so here more than once. If you were not being obstinate, I am sure you would have seen it yourself. For example, your random-walk model is “outside the laws” in this sense because it contains no empirical input whatsoever (at least with regard to the results that do not depend on the values of the parameters). So too, a random drawing of one chain from all the theoretical possibilities (not only the “living” ones) is a model that is outside the laws. The laws focus you more toward the “living” ones. The drunkard without the wall, and blind typing without the programmer’s help, are outside the laws. I have defined this again and again, and you insist on ignoring it. But indeed none of this is connected to the discussion of this passage. 2. I repeat for the who-knows-how-manyth time: on the contrary, this model describes the idea of evolution quite well (a random process that undergoes acceleration, or a moderation of slope, by circumstances and constraints). True, you will not find within the gutter what represents the short-tailed grasshopper or the triangular-tailed creature, because this is not a model of all evolution but of its basic idea. This is the main description given by Gould and Dawkins of evolution. I wrote that it is mistaken only as a model intended to explain why evolution is a self-sufficient explanation (without the need for an external factor). 3. It seems to me that here you are simply not being honest. Ask the ordinary reader how he understands that sentence of yours. In addition, see also your less polite and less indirect words in the talkbacks. But it seems once again that you are fond of Tosafot-style interpretations rather than Rashi-style ones (=the plain meaning of the texts under discussion). By the way, I completely agree with the claim you quoted here: “About this argument I can say either that I understand nothing about evolution, or that Rabbi Dr. Abraham understands nothing about evolution (or that neither of us understands anything about it).” The correctness of my argument entails one of the components of the disjunction in the concluding clause (although I assume we disagree about which one). As a mathematician, you surely know that if Q holds, that also satisfies “Q or P.” Since you keep returning to the methodological distortion I pointed out—criticizing this chapter as though it were an article that makes context unnecessary—I assume you will forgive me if I do not enter into this foolish discussion (as you yourself defined it). You expect a text like this to present probability calculations in a popular piece, when the facts (that we are dealing with an improbable slope, if one does not take into account the moderation of the laws of nature) are agreed upon by everyone, including Dawkins and Gould and anyone with even a slight familiarity with the subject. The sentence you quoted says that in the evolutionary process in the style of Dawkins and Gould (!) we do not have a wall, for they (as atheists) claim that a full explanation of the phenomenon of life requires no additional factor beyond the evolutionary explanation. The dispute is about that and not about the correct model of evolution. On that we all agree (except perhaps you). But to understand this one has to see the context, which you did not do. 4. Indeed, I did not read Gould, just as you did not read my remarks before criticizing them. The difference is that I needed only the principle (and therefore there is no need to verify details, and there is no problem in using a secondary source, especially one by an expert like Dawkins), and I was right; whereas you criticized the details (and therefore you needed to read the context, because this is not an article but an illustrative excerpt) and were mistaken. On 5-6 I have nothing to add.