Answer

Hello.
Gadi Alexandrovich is a very intelligent person, and his blog is truly fascinating. This article, to the best of my admittedly biased judgment, is unfortunately a failure, among other reasons because he did not understand my point since he had not read the book, and also because he chose to interpret the parable too generously. You can always take nonsense someone else said, turn it into a different argument, and explain that he said profound wisdom. But unfortunately, that is not 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, while he is making a claim within the laws).
I wrote a detailed response to that post which appeared on a site established by one of my students, but it disappeared from the internet. Some of the responses published there appear here on the site, but I do not remember whether that includes my response to this post.
——————————————————————————————
Questioner (Gadi Alexandrovich):
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 additional interesting mathematical content in the book, so there will not be any more posts about it). The critique, as stated in the post, is of a specific article the Rabbi published on the Ynet site and which is based on an excerpt from the book. That excerpt contains nonsense. Maybe one can take the nonsense written in the article, convert it into another argument, and explain that it contains sublime 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 to identify what Gould’s argument was meant to be (I would be happy to get an exact reference to see whether my guess was correct). As I note there, if my guess is correct, Gould’s argument is very problematic, not “sublime wisdom” (in fact, I guess Gould did write something smart, and the Rabbi does not do him justice with the half-mention he gives him).

3) It is a shame that the Rabbi did not also write the detailed response to the post as a comment on my own post, in which case it would not have been lost.
——————————————————————————————
The Rabbi:
Hello Gadi.
First of all, thank you for engaging. Since I was asked, and have now been challenged again, I cannot help but write something more detailed. Especially since on Tisha B’Av one does not study Torah, so I have a golden opportunity to deal with these matters, and perhaps thereby contribute something to redemption and 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 perhaps I needed to spell it out more. So I ask forgiveness for the length (as the great Mr. Mark Twain said: sorry for the length; I did not have time to write briefly).

Clarifying my point about the importance of context
Let me begin by saying that in the subtitle of the Ynet excerpt you critiqued (which was all written by the editors, not by me, and I share your criticism of the connection they made there to Einstein), it is made very clear that this is an excerpt from a book intended to give a small taste of its contents, not an article. You yourself mention this, so apparently you did not miss it. It seems a bit strange to me that you treat it as an article that is supposed to make claims and be self-contained, and critique 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 will now try to show, it also fails on its own terms (that is, even without resorting to the context and the full book).

A methodological note: the principle of charity
As I wrote in my short response here on the site, in the course of your defense of Gould you translate Gould’s parable and substitute another parable in its place, and then you criticize me for misunderstanding the parable and evolution. This methodology is highly problematic on its face. Before I get to the details, let me first make a methodological remark about your way of arguing.
Donald Davidson (a well-known American analytic philosopher) once formulated what he called “the principle of charity,” according to which one should interpret the person one is criticizing in the way most favorable to him and only then argue with him, and that is what you did. But I would add two reservations to this nice principle: 1. The charitable interpretation must remain reasonably faithful to the source (that is, there must be a reasonable possibility that this is indeed what the author meant). It is not reasonable to propose an interpretation that completely changes the original meaning (otherwise it becomes impossible to critique and argue, because every failed argument in the text under discussion will be replaced by a brilliant argument invented by the critic, and Zion will thereby be redeemed). 2. If you do that for Gould—that is, replace his argument with another one that withstands criticism—why did you not choose to do the same for me?! For example, to conclude that although Gould probably meant your parable, I probably understood him according to what I wrote and therefore criticized him justifiably.
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 am drawing on a secondary source; I did not see Dawkins cite Gould’s original source). But in that case, what you should do is simply say this: Abraham’s critique is correct, but I do not think it is likely that this is what Gould wrote. Maybe he meant to say such-and-such, in which case Abraham’s critique falls apart. But I do not see how you permit yourself to put in Gould’s mouth something completely different from what I quoted him as saying without knowing that this is what he said, and then claim (albeit gently) that I understand nothing about evolution or any other field.
Perhaps you will say: but this is precisely applying the principle of charity! Your interpretation treats Gould charitably, as Davidson instructs. But you could also assume (certainly if you are acting according to the principle of charity) that I too know that the evolutionary tree does not consist of just a single path such that if it dies, the process is over. I too know there are masses of attempts and lots of drunkards setting out on the road. But unfortunately 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 also deserve the protection of the principle of charity? 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 parable: between outcomes known in advance and outcomes dictated in advance
Unfortunately I do not now remember the source of Gould’s parable. As far as I recall, Dawkins brings it in one of his books (I will try to look again. It was a long time ago). In any case, as I wrote, its purpose is to show that there are processes that look random and yet whose outcome is dictated in advance because of external factors (circumstances) that speed them up / accelerate them. Dawkins uses this to attack the assumption of the physico-theological argument for the existence of God. It does indeed look like a foolish argument, and as I will show immediately it works as an anti-atheistic boomerang, but it recurs not infrequently in atheist holy writ, and in my view it actually illustrates very well the core of the physico-theological argument, which is why I chose to go after that particular excerpt.
You “translated” this example into a random walk, what you called the gambler’s ruin phenomenon, where there is an outcome known in advance (but not dictated) in advance. As a physicist I prefer to look at this 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 set of equally spaced points along the x-axis (for simplicity, let us say the integer points on the axis). A given drunkard starts from some point on the axis, say x=n (what you called the initial condition), and at every place where he is he has a probability p of staggering right and q of staggering left (the process is Markovian, that is, memoryless, and let us assume the probabilities are constant at all points and times). The known result you proved is that no matter where he starts, he will eventually cross the origin (x=0) at some time (as I recall—I am a bit rusty—at least when p=q the time is proportional to n^2).
Your process is completely random, but its own properties (not external constraints) create a chronicle of a known-in-advance result. Precisely for that reason it bears no resemblance in any sense to the drunkard parable, which deals with the influence of constraints and accelerators, and therefore your translation, though charitable to Gould, is irrelevant to the discussion. You propose another parable instead of his, one that illustrates a different phenomenon, then analyze your parable, and finally criticize my remarks, which dealt with his parable. It seems to me I can hardly be blamed if I say that this methodology strikes me as problematic.
By the way, 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 unless enough drunkards set out. To see in such a model an alternative to the existence of an intelligent factor, one has to show that these conditions do in fact obtain (that there are enough drunkards and/or that enough time has passed). I note that various calculations that have been made claim they do not obtain (regarding abiogenesis, even Dawkins argues in favor of the thesis of a “lucky accident,” and de Duve and many others reject this on the basis of calculating the number of attempts and the timescales; see also the remarks at the end), but that is not our topic.
Let me add one more clarification to the claim that emerges from the drunkard parable. When I looked for the source of the 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 on, a very similar parable in which Dawkins discusses the formation of a meaningful sentence through a random process of keyboard strikes (with a monkey dancing on it). Let us say we want to create the sentence “Methinks it is like a weasel” (in the original experiment I discussed in the Ynet article, the phrase was: tobeornottobe) by random keystrokes on the keyboard. This is of course a computer 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 final forms) plus a space, then there are 28 possibilities at each keystroke; the probability of obtaining the whole sentence is therefore 28^(-21). That is something like 1 divided by a number with thirty zeros, in other words truly negligible. So 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 as far as one-step random drawing goes. But what happens in the process he there calls “cumulative selection”? It is a process in which the string produces many “offspring,” from among which we choose the one most similar to the target string (!), no matter how slight the similarity. [I did not see there a specification of how many offspring are produced at each step.] Astonishingly, Dawkins reports, in such an experiment one reaches the target after a few dozen “generations” (around the 50th or 70th generation). As I recall, in the computerized experiment with tobeornottobe they did something slightly different: every time they got a correct character in the correct place in the string, they froze it and redrew only the rest. And lo and behold, there too the process became dramatically shorter.
Dawkins’s conclusion (p. 65 there): There is therefore a huge difference between cumulative selection (in which every improvement, however tiny, serves as a basis for future building) and one-step selection (in which every new “attempt” starts from scratch). If evolutionary progress had had to rely on one-step selection, it would never have gotten anywhere. But if there is some way in which the blind forces of nature could set up the necessary conditions for cumulative selection, then the results would be strange and wonderful. In fact, that is exactly what happened in our world, and we ourselves are among the most recent, if not the strangest or most wonderful, of those results.
That is, he is speaking about a non-Markovian process (one that has memory. Each step in the drawing remembers the previous results and depends on them). In fact, it not only remembers the past but also knows the future (what the target is, since within the process it repeatedly compares itself to it). That is in total contrast to the random walk parable you brought.
Note that in his parable we are dealing with an outcome dictated by external constraints, not a random outcome known in advance (as in your random walk). His claim is that evolution is not just a collection of random (Markovian) draws but draws under external constraints that remember what has been and know what they are moving toward, and thus dictate the result 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 outcome. So here you have our much-maligned drunkard parable itself, in which the wall brings the random drunkard to our desired destination. Is it also right, regarding Dawkins’s own words, to apply a charitable interpretation and change his parable into something Markovian, without constraints and without memory?
My claim is that a parable like this drunkard one is very common in these discussions, and therefore it is not really so important what exactly Gould said. And from this it follows that there is also no basis for your estimate that he could not possibly have said it, and still less for the generous “translation” you suggested on his behalf. Either way, my remarks critique 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 known in advance of a random walk. As far as I am concerned, this is a critique of Dawkins and not of Gould (see also the remarks at the end).

The conclusions from a process whose outcomes are dictated in advance
So we have returned to discussing the parable whose outcomes are dictated in advance by external constraints (and not merely known in advance, as in a random walk). I doubt I need to explain to readers—and certainly not to you—the theological significance of Dawkins’s example. What he demonstrates is that while the evolutionary process is not probabilistically possible, if we add a guiding hand (teleological, that is, result-directed, in a very blunt way)—namely, a programmer who ensures that the computer’s drawing reaches our desired destination—it becomes something possible. Does that remind one of the drunkard parable? Absolutely. The drunkard too cannot reach some target by random walking, but if one creates circumstances around him (a gutter and a wall) that ensure he arrives, then indeed he will arrive. And in the lesson of the parable: a random drawing of a “successful” protein chain is improbable, 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 probable.
These parables are used by Dawkins when he comes to refute the physico-theological argument, but in fact this is exactly the physico-theological argument: it claims that for an improbable process to succeed, a guiding hand is required, and these parables only strengthen that argument rather than refute it. And in the lesson of the parable, in order for the evolutionary process to occur with a reasonable probability there must be a guiding hand that sets the rules of the game so that the result will emerge. With different rules of the game, or without any rules at all, it probably would not happen. The physico-theological argument claims that this guiding hand is God (for present purposes one may say that this is basically a definition of Him rather than a claim about Him).
Note that the parables of Dawkins and Gould do not rely on there being many repeated attempts, as you put into his mouth. They are talking about the influence of a guiding hand, laws, or circumstances, affecting the process from the outside. The focus of the discussion is: what are these external “circumstances”? Who created them? The neo-Darwinians say these are the laws of nature (which cause the formation of random mutations and the genetic inheritance of their traits, and in fact the whole evolutionary process, thereby directing it to its goal and making the assumption of an intelligent factor superfluous). The random walk proceeds within them and under their influence, and therefore it can reach its goal. That is the scientific explanation, and I fully accept it. But my question is on the theological-philosophical, extra-scientific plane: where did these so very special laws come from, without which none of this would have happened? There is a guiding hand here, leading the drunkard (by means of the wall and the gutter) to his destination. If there were no wall and gutter there (in Gould), and if there were no comparison of the string to the desired string (in Dawkins), the desired result would not be obtained. As we have seen, Gould and Dawkins themselves manually inserted external elements into the system so that randomness would lead to the desired outcome. In Dawkins this is even more blatant, because he inserts the desired outcome itself into the process (by comparing at each stage to the target string). That is really an own goal, because he describes evolution as something goal-directed that was planned in advance to get there. He puts God inside and then claims that we no longer need Him. [Like that dear Jew who cannot find parking and turns to God in heartfelt prayer to help him. In his distress he promises that from now on he will devote his life only to Torah and commandments. And then, right next to him, a parking spot opens up. Our friend is not fazed, and immediately turns back to God: “No need, thanks, I managed already.”]
Let us now return to the lesson of the parable. Evolution is a description of a process that proceeds within the laws (=the wall and the gutter), and they are what make sure that it “succeeds.” Without them it would not happen. I now ask where the laws themselves came from. The physico-theological argument concludes that it is reasonable that there is a guiding hand leading the evolutionary process to its goal. So why be surprised that it really gets there? These parables are not a refutation of that 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 arose on their own or that they always existed and their character was determined arbitrarily, that is perfectly fine with me. In that case the physico-theological argument really will not persuade you (any logical argument addresses only those who accept its premises). But note that you are assuming in advance that something special (=the laws) can arise blindly. If so, what does all the evolutionary pilpul add to 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 directing factor). And if you assume that this is not likely, then you do accept it. Either way, evolution is irrelevant to the discussion, and the drunkard or monkey-and-keyboard arguments even more so.

A few closing 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 came into being. One can also discuss whether the laws are special. Dawkins deals with this later on in The Blind Watchmaker, and in my view he is wrong there too, and badly so. One can also discuss whether the thesis of an intelligent factor solves the problem, and whether the term has any meaning at all. I discussed some of these things in my series of Ynet articles. But all of that already goes beyond the discussion of the excerpt here. Here I wanted to explain what I meant in that specific excerpt and clarify why your critique does not address my actual point. For continuing the discussion I can only refer the reader to my Ynet articles and to reading the book.
B. As far as I know, Gould too is an atheist, but he disagrees sharply with Dawkins (sometimes very stormily) about the status of God with respect to evolution. Dawkins claims evolution proves (almost certainly) that He does not exist, whereas Gould thinks the questions are independent of one another (perhaps evolution makes the claim of His existence unnecessary, but it does not prove anything about Him). I too think the questions are independent, because as I showed above the dispute depends on the starting point (can a complex thing arise / exist without an intelligent directing factor?), and evolution neither adds nor subtracts anything on that issue. I explained this above. What I added concerning the strengthening of the physico-theological proof is that if the starting point is that it is unlikely that a complex thing could exist without an intelligent factor creating it (that is what this argument assumes), then evolution strengthens the physico-theological argument. Of course whoever 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 (though in my opinion the assumption is somewhat irrational). Therefore in any case evolution is not connected to the discussion. The matter is clarified more in the book itself. My argument is mainly with Dawkins, and from my point of view the parable Gould brought is not important (though it is not exact). What concerns me here is mainly the use Dawkins makes of it to attack the thesis of the existence of God.
C. Of course this whole discussion concerns one drunkard, and as you rightly noted, in the evolutionary process there are many drunkards. Note that in Dawkins’s parable of the target string this has already been taken into account, since many drawings are made there and not just one. But as I explained, even in the drunkard parable the point is not this effect, but a situation created 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 parable ignores the number of drunkards, and therefore I ignored it as well (though I did add a short discussion of a paper wall with rigid points that hints at this aspect).
Incidentally, in my book I cite a calculation by de Duve showing this also in the evolutionary context (actually in the context of abiogenesis—that even if one takes into account the large number of attempts made, the probability of forming a “successful” chain is negligible. He gives a rough estimate there of how many attempts were made), and the question is treated there at length 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 Gould and Dawkins know that too.
D. It is important now to note that if this response had been long (purely hypothetically, of course), and Ynet had only brought the seventh paragraph from it to illustrate what it was about, would it be appropriate to critique what was said in that paragraph as though it were an article making a claim? That is basically what you did in your post. But, as I said, my argument here is that your critique also does not hold water on its own terms, that is, even without entering into the whole book and the context. In my short response on the site I noted that the problem is both that you did not read the book and because of 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 parable).
——————————————————————————————
Questioner (Gadi Alexandrovich):
With your permission, I think it would be better to focus the discussion. My experience is that extremely long responses spill far beyond the bounds of the issue under discussion, and there is no reasonable way to address them.

So to the point: I am surprised to discover that you brought 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 with the parable, 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 several focused questions. A focused and short answer to them will help the discussion.

1) Are you claiming this is not the case?
2) Are you claiming that Gould thinks of the drunkard as being within a single organism?
3) How, in your text, do you understand the drunkard parable? What does the drunkard correspond to for you? A single organism? A population? The whole process? What is the meaning of the gutter, and what is the meaning of the “paper wall” for you?
4) You say, “In the evolutionary process we do not have a wall that ensures that each time the drunkard will be returned to the path.” Why is this important? As I explain in the post, the wall is devoid of significance. Mathematically, the behavior of the drunkard-with-wall and drunkard-without-wall models is similar: with 50:50 probability the drunkard will eventually fall into the gutter (whether or not there is a wall), and if there is a bias in favor of walking away from the gutter, it is not guaranteed that the drunkard will eventually fall into the gutter (whether or not there is a wall).
——————————————————————————————
The Rabbi:
Hello Gadi. With your permission, I will skip the rebukes and counter-rebukes.

A. I entirely agree that Gould is talking about a population. That is exactly what I wrote (that for purposes of the discussion one may say that the effect of many drunkards is included in the model).
B. You are getting into unnecessary hairsplitting. The parable is meant to say that sometimes external constraints accelerate the random process and focus it (moderate the slope of the improbable mountain, in Dawkins’s phrase). That also emerges from Dawkins’s own parable about the jumping monkeys.
C. Your other comments concern your model, and as I explained, it is irrelevant to the discussion, and not for nothing do neither Dawkins nor Gould (apparently), nor little old me, deal with it. I must say that in doing so you are repeating the same methodological error about which I went on at length in my remarks (so perhaps after all it would have been worthwhile for you to read them), and therefore I will not enter into a discussion of it.
D. In my parable it is clear that there is a difference between the model without the wall and with the wall. It seems to me simple probability calculations would be agreed upon by both of us, and there is no point entering into quizzes about them.
E. I will now explain again why your model is irrelevant 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 from probability calculations alone (and does not really depend on the values of the parameters, as you correctly showed). Hence there is no representation there of the influence of any laws of nature. If one assumes your model models evolution, it turns out that evolution is a branch of mathematics and not of empirical science, which is of course nonsense. I assume we will 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 modify some detail or other) as well as the jumping-monkey model (of Dawkins) are indeed the correct models for evolution (except for corrections I pointed out in my remarks, but clearly we are not talking about cleansing away environmental constraints as you suggest). The external constraints in these models (the wall and the programmer), which do affect the result, and necessarily so, express the influence of the laws of nature within which the random process takes place.
But as I argued, precisely because of that these models well illustrate why the evolutionary picture does not exempt us from the conclusion that there exists a guiding hand (unless one accepts that complexity can arise by itself, in which case again evolution is irrelevant to the discussion).
——————————————————————————————
Questioner (Gadi Alexandrovich):
Let us focus further.

If you agree that “Gould is talking about a population,” I want to understand, before we can continue the discussion, 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. Every walk in the direction of what is not evolutionarily viable (that is, toward the wall) leads to a dead end of the process, meaning the extinction of the creature or of its evolutionary descendants.”

1) “The extinction of the creature” — what creature is being referred to if we are speaking about an entire population?
2) If you indeed have in mind an entire population, what is the analogy of the paper wall meant to represent? Is it meant to describe an evolutionary change that causes the extinction of an entire population?
——————————————————————————————
The Rabbi:
Indeed. If one does not take into account the “external accelerators” (=the wall), then the fate of the entire population (=the gene) is extinction. A dead end in the evolutionary process does not refer to an individual organism but to a population or type (=the gene). Evolutionary development extinguishes most organisms and leaves the strong ones (the survivors). But even the survivors survive only thanks to the wall (=the laws of nature), and without it they would all reach a dead end. Exactly as Dawkins explains that the slope of the mountain is improbable (before it is moderated). He does not mean a single organism climbing the mountain but a gene.
——————————————————————————————
Questioner (Gadi Alexandrovich):
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. Later you say, “Let us add to our model the fact that there is a tiny number of points on the wall made of hard stone, and hitting them will send the drunkard back to the sidewalk.” Can you give real-world examples of such an evolutionary wall?
——————————————————————————————
The Rabbi:
As far as I know, a contradiction is always between two things. I wrote that the wall is made of paper. Therefore? Where is the second horn of the dilemma? As for your remarks: first, on the level of the genotype. If you look at the collection of all protein chains, there are masses of them (an ocean). Of these, only a completely 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 from one of these islands to another. 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 in no way happen by an ordinary random walk (without constraints) were it not for laws of nature (the wall) that ensure it happens, meaning that there will be a reasonable number (it can still be very tiny, but enough for the gene to survive) of jumps in the ocean from the island one is on to other “living” islands. Those laws turn the wall from a paper wall (with a few hard points) into a hard wall, or alternatively ensure that a sufficient number of jumps strike its hard points. And here is an example on the level of the phenotype. Look at the case of the finches’ beaks. There was a drought on the island and all the plants they fed on disappeared. All that remained were plants whose cracking required an especially strong beak, and thus the finches with strong beaks survived and passed this trait on to their descendants. It could have happened that all the plants would disappear, or that there would be no birds with a strong beak, 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 if this trait were selected in the natural process it would not pass to descendants and the finches would become extinct. The laws of evolution (formation of mutations + selection + genetics) moderate the slope of the improbable mountain and ensure that mutations produce, among other things, something nearby, such as a finch with a strong beak, and/or that not all the plants always disappear. Thus the finches’ gene survives and passes to the next generation. If this were merely a random walk (without the accelerating influence of the laws of nature), it is not likely that this could happen.
——————————————————————————————
Questioner (Gadi Alexandrovich):
I understand (I do not agree, but at least I understand).

Is your claim that Gould claimed this was a completely random walk? Prove it.
 
Well, I decided it would be better if I did the research that up to now has not been done here. Gould’s use of the parable comes from his book Full House: The Spread of Excellence from Plato to Darwin. I will bring the relevant section in full. Too long; didn’t read: as I thought, Gould is not trying in any way to claim that the drunkard parable describes evolution at all. He brings it as a simple mathematical example of how, in a random process (one in which there is a 50:50 probability in either direction), a preference toward a certain direction (the gutter) is created.

I think he is mistaken in his interpretation. He brings the wall as the reason for the creation of the preference. As I understand it, the wall has nothing to do with it at all and could have been omitted; the reason a “preference” is created is that from the moment one reaches the gutter, that is it—you are stuck there. If there were no gutter, the process would reach arbitrarily large distances in both directions and that would be the end of it. In other words, I think Gould is using an incorrect mathematical metaphor here, though with a more careful mathematical analysis of the drunkard-with-wall situation maybe one could get something that matches what he wanted to say.

If so, what was done in the Ynet article is of course unfair. The article attacks the parable as if the parable were meant to describe evolution. According to Gould, explicitly, the parable was not meant to do that but rather to clarify a more basic point.

(Personally I think any attempt to describe evolution by means of this parable is completely ridiculous, which explains the foolish discussion going on 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. "
——————————————————————————————
The Rabbi:
Hello Gadi. We began with the claim that I understand nothing about evolution, mathematics, or anything else, and that I talk nonsense. Now I get the impression that we are in a somewhat different position. I will try to explain again the state of affairs as I understand it. If you want to continue the discussion (the foolish one, in your own definition, with which I completely agree), please tell me what exactly your original claim in your post was about. I would appreciate it if at this stage you did not raise new claims, but only explain what you meant when you said that I understand nothing and talk nonsense (within the framework of the excerpt published on Ynet). After that we can discuss additional things if you wish. 1. Background to my claim: evolution is basically a kind of random process that by simple probabilistic calculation (=outside the laws) has almost no chance of being realized. The fact that it is indeed 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 so on). In this respect evolution is part of the natural sciences and not of mathematics. My basic claim in the book is that if there are external constraints due only to which we got this far by blind and random walking, it is reasonable to assume there is an intelligent factor that created them and thereby in fact caused this outcome. As stated, this claim is not necessary but very reasonable (in my view). Whoever is 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 reasonable ones in this case, in my humble opinion). 2. Up to here the background, and now to the excerpt in question published on Ynet. I remind you—your remarks dealt only with it (since the background probably was not known to you at all): A. There I brought the drunkard parable and argued that it expresses the idea that a random process can reach its goal with the help of external accelerators / constraints. A claim Gould himself makes in the passage you quoted, and Dawkins does so in countless places as well. Those accelerators are basically the laws of nature mentioned above. In my remarks to you on my site I added Dawkins’s parable of the random creation of a character string, which says exactly the same thing on the conceptual level. B. Afterward I argued that these parables do indeed correctly describe evolution (see the background in section 1), but the hitch is that they do not refute the physico-theological argument about God; rather, they illustrate its logic very 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 needed. That is more or less what I wrote there. 3. Now to your post: you argued against me in general that my remarks in this excerpt (that is, the last two paragraphs A-B above. You were not familiar with the background at all) are a mathematical misunderstanding, that I know nothing about evolution, and that I am talking nonsense. It seems to me that this is a fair summary, even if a bit concise, of what you said about me. In addition, you offered a different and somewhat fanciful explanation of Gould’s parable, one that even you now agree is not really what is written there. You also agree that Gould was mistaken in exactly what you (mistakenly) attributed to me, namely saying that the wall affects the result. In the parable as I understood it, it indeed does affect it. 4. So what remains of all this? At present it seems that all that remains is to interpret the holy writ of Gould and determine whether Gould told the parable precisely one way or another. This does not really concern the substance of my claims, and certainly does not point to any mathematical or scientific misunderstanding such as you attributed to me. Therefore it does not in any way touch the heart of your post. But if nevertheless for some reason you would like to know my opinion of Gould’s remarks, which as I say is not really important to me, I still stand by everything I wrote about them. Gould is indeed describing the idea of evolution in this parable (as he explicitly writes here), he uses it to show that external constraints can focus a random process, and of course he also inserts the wall into it (which according to you has no effect). Therefore, in response to your question in your last message in this thread, in my view he is not dealing with pure random walking. I will now only add that if, as an atheist, he assumes there is no guiding hand, then in my view his remarks are highly implausible. I can only agree that the discussion here looks somewhat petty and foolish, as you wrote, for from all the grand ideas and emphatic accusations we have arrived at clarifying the purchase of that righteous man (Gould). But it seems to me that this is not really my fault. 5. And one more reminder: I cannot help but return to the methodological problem I pointed out in my long response, and also to your assertion about a contradiction between one statement of mine (that the wall is made of paper) and… to this day 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 by me), I would be glad and appreciative if you saw fit to insert some correction or apology around the intemperate and unfounded post, which is very uncharacteristic of you. Precisely because I value your writing very much, and apparently others do too. Even if you do not find it appropriate to do so—there is no problem at all. We can part as friends after our brief chavruta here. It was a pleasure to meet.
——————————————————————————————
Questioner (Gadi Alexandrovich):
1. This background is clear. I think it amounts to misleading the readers, because it is impossible to define anything “outside the laws,” though I would be happy to see you define *formally* a random process *for evolution* that is *outside the laws* so that one can perform on it the sort 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 parable, which Gould is not trying at all to claim describes evolution, and say it is *mistaken* (“The problematic nature of this parable lies on two different levels…”, “Gould’s absurd model”).

Here, in my view, you seriously mislead the reader. You take a toy model that nobody 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 ridiculous. You are using an utterly ridiculous and simplistic model to talk 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 fine to talk about evolution by means of this model, and one just needs to make a few corrections (for example, your paper wall). After all, Gould is one of “the good guys.” This is a serious deception of the readers, and I very much hope that was not your intention; but if it was not your intention, I cannot understand why you are talking about this model here in the first place. Gould brought it in order to make a *very specific* claim, one that you do not refute and do not even talk about 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 presuming 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 offered of Gould is fictional, because at the time I mistakenly thought that Gould was indeed trying to use the drunkard parable to describe evolution. I blame your article for creating that misleading impression. If you want, I can correct my post so that it clears Gould of the accusation of trying to use the drunkard parable as an evolutionary model, and explain that this is a misleading move made 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. Possibly. But in order to show that, you will need to explain in detail what they mean and how that meaning follows from the text; not to offer other ideas that appear elsewhere in your writings and contradict your text. In the text it says, for example, “In the evolutionary process we do not have a wall that ensures that each time the drunkard will be returned 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 this: want to rescue the article? Take the three paragraphs quoted in my post, and write an explanation for them. The explanation should include: the exact 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 it.

For example, what is an “evolutionary step”? Are we speaking of a single mutation that appears in a single individual from the group? If so, why would such a step, if it leads to the creation of a “non-living mutation,” stop the evolutionary process at the group level? (It would not.) If not, how common is it? Do these probabilities correspond to the probabilities in the drunkard mathematical model, where the probability of walking toward the wall is identical to the probability of walking in the other direction? Etc., etc.

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. With that, in my opinion the interesting part of this 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 hits it, and describing the wall as made of paper such that everyone who passes through it becomes extinct. Later in your article you change this model into a wall with “a tiny number of points on the wall made of hard stone,” and that resolves the contradiction (that is, it replaces the contradictory models with a unified one), but to see that I had to make the effort and reread the article.

This sharpens what bothers me in your writing: you begin unnecessarily with mistaken models, without even hinting that they are mistaken, and after lengthy engagement with them that is not actually useful for anything, you quickly move on to talking about the less mistaken models. Another problem is that even the less mistaken model does not necessarily match reality, but we have already talked about that.

6. As I suggested in section 3, I am willing to correct in the post my attempt to guess what Gould meant, and clarify that your article misled me into thinking that Gould was actually trying to give an evolutionary model with the drunkard parable, whereas in fact he was not.
——————————————————————————————
The Rabbi:
Hello Gadi. Unfortunately, you are fleeing into foreign and irrelevant territories, and that is a shame. Things I have already explained well, over and over, you keep demanding to be explained again. You demand a calculation where no calculation at all is required in order to understand the claim, and you send me to write Rashi and Tosafot on my own words and on Gould’s words, even though in your view they are mistaken (and in mine they are not), and even though you admitted that your own understanding of them was mistaken as well (though by a strange sort of rhetoric I alone am to blame for this). I repeat for the umpteenth time that these models are not meant 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 achieving a “successful” result. This is the central idea of evolution, and on this there is no disagreement between me and Gould and Dawkins and anyone else who understands the subject. Almost all of Dawkins’s books, as well as some of Gould’s writings, are devoted to this, and the model illustrates it very 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 so insistent, I am sure you would have seen it yourself. For example, your random-walk model is “outside the laws” in that sense because it contains no empirical input at all (at least regarding the results that do not depend on the parameter values). Likewise, drawing one chain out of all theoretical possibilities (not only the “living” ones) is a model outside the laws. The laws focus you more in the direction of 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 all this is not connected to our discussion of this excerpt. 2. I repeat for the umpteenth time: on the contrary, this model describes very well the idea of evolution (a random process that undergoes acceleration, or slope-moderation, by circumstances and constraints). True, you will not find inside the gutter whatever represents the short-tailed grasshopper or the triangular-tailed whatchamacallit, because this is not a model for all of evolution but for its underlying conceptual idea. This is the main thrust of Gould’s and Dawkins’s description of evolution. I wrote that it is mistaken only as a model meant to explain why evolution is a self-standing explanation (without need for an external factor). 3. It seems to me that here you are simply not being honest. Ask the average reader how he understands that sentence of yours. In addition, see also your less polite and less indirect remarks in the talkbacks. But it again seems that you prefer Tosafot-style interpretations over Rashi-style ones (=the plain meaning of the texts under discussion). By the way, I entirely 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).” If my argument is correct, then one of the elements in the disjunction at the end is satisfied (though I assume we disagree about which one). As a mathematician you certainly know that if Q holds, it also satisfies “Q or P.” Since you keep returning to the methodological distortion I pointed out—the critique of this chapter as though it were an article that eliminates the need to resort to context—I assume you will forgive me if I do not enter into this foolish discussion (as you yourself defined it). You expect such a text to present probability calculations in a popular essay, and this when the facts (that we are speaking about an improbable slope, if one does not take into account the moderation produced by the laws of nature) are agreed by everyone, including Dawkins and Gould and anyone even slightly familiar with the subject. The sentence you quoted says that in the evolutionary process according to 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 argument is about that, not about the correct model for 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 was no need to verify details, and 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, since this was not an article but an illustrative excerpt), and you were wrong. On 5-6 I have nothing to add.