Response to a review of "God Plays Dice"
Ynet – 2011
I recently came across In review on The Rabbi's article About God playing dice on YNET.
What does the rabbi claim in response to the criticism?
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Rabbi:
Hello.
Gadi Alexandrovich is a very intelligent person, and his blog is really fascinating. This article, to the best of my biased judgment, is unfortunately a failure, partly because he did not understand what I said because he did not read the book, and also because he decides to interpret the parable too generously. You can always take someone else's nonsense and convert it into another argument and explain that he said words of supreme wisdom. But what can you do, that is not what Gold said. And even if he did say that, he is wrong as I explained in the book (because the proof is a contradiction of the laws and he is making a claim that is within the laws).
I wrote a detailed response to this post that appeared on a website my students set up, but it has since disappeared from the web. Some of the comments posted there appear on the website here, but I don't remember if they include a reference to this post.
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Asks (Gadi Alexandrovich):
Some notes:
1) The criticism is not about the book (which I did not read when writing the article; I have since read it and I do not think that the book contains any additional interesting mathematical content, so there will be no posts about it). The criticism, as stated in the post, is about a specific article that the rabbi published on the Ynet website and is based on an excerpt from the book. This excerpt contains nonsense. Perhaps one can take the nonsense written in the article, convert it into another argument and explain that it is a statement of supreme wisdom, but the text written in the article is nonsense.
2) My article makes no particular attempt to interpret Gold. There is not enough text in the passage the Rabbi posted to make it possible to identify what Gold's argument was (I would be happy to receive an exact reference to see if my guess was correct). As I point out there, if my guess is correct, Gold's argument is very problematic, not "higher wisdom" (in fact, I guess Gold did write something wise, and the Rabbi does not do him justice with the half-reference he gives).
3) It's a shame the rabbi didn't also write the detailed response to the post in response to my post, then it wouldn't have been lost.
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Rabbi:
Hello, Gadi.
First, thank you for your consideration. Since I was asked and now challenged again, I can't help but write something more detailed. What's more, on Tisha B'Av, Torah is not studied, so I have a golden opportunity to deal with these matters, and perhaps in doing so I will contribute something to the redemption and the building of the Temple (the vegetarian one, as I hope).
Since I saw that people I consider very intelligent did not fully understand my words, I thought that perhaps I should elaborate on them. Therefore, I apologize for the length (as Moharram Mark Twain said: Sorry for the length, I did not have time to write a short one).
Clarifying my words about the importance of context
I will start by saying that the subtitle of the section in the Wit that you criticized (which is entirely from the editor and not from me, and I share your criticism of the link they made there to Einstein) makes it very clear that this is a section of a book intended to demonstrate in a nutshell its content, and not an article (you yourself mention this, so you probably didn't 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 criticize it without knowing and understanding the background and context in which the things were said. This is what I meant when I wrote that you haven't read the book and therefore your criticism is flawed. But as I will try to show now, it also fails from within (i.e. without needing the context and the entire book).
Methodological Note: The Principle of Grace
As I wrote in my brief response on the site here, in your defense of Gold, you translate Gold's parable and substitute another parable in its place, and now criticize me for misunderstanding the parable and evolution. This methodology is very problematic on its face. Before I get into detail, I will first make a methodological comment on your line of argument.
Donald Davidson (a well-known American analytical philosopher) once formulated what he called the "principle of kindness," according to which it is appropriate to interpret the person you are criticizing in a way that is most beneficial to him and only then argue, and that is what you did. But I would add two caveats to this pleasant principle: 1. The beneficial interpretation must be reasonably faithful to the source (meaning that there is a reasonable possibility of assuming that this is indeed what the author intended). It is not reasonable to propose an interpretation that completely changes the original meaning (otherwise it is impossible to criticize and argue, since every failed argument in the text being criticized will be replaced by a brilliant argument of the critic's own, and comes to the point of salvation). 2. If you do this to Gold, that is, replace his argument with another argument that stands up to criticism, why didn't you choose to do the same to me?! For example, to conclude that although Gold probably intended your example, I probably understood it according to what I write and therefore criticized him rightly.
Furthermore, even if you suspect that Gold intended something else or even explicitly said something else and I misunderstood him, it is certainly possible that you are right (since I too draw on a secondary source. I did not see in Dawkins the reference to Gold's source), but in that case what you should do is simply say this: Abraham's criticism is correct, but it is unlikely in my opinion that this is what Gold wrote. Perhaps he intended to say such and such, and then Abraham's arguments for criticism fall flat. But I do not see how you allow yourself to put into Gold's mouth something completely different from what I took from him without knowing that this is what he said, and then claim (albeit gently) that I understand nothing about evolution or any other field.
You might say, this is an application of the principle of grace?! Your interpretation is biased towards Gold, as Davidson commands. You can assume (certainly if you act according to the principle of grace) that I also know that the evolutionary tree does not consist of only one path, and that when it dies, the process is over. I also know that there are many attempts and many drunks who set out. But what can be done? This is not Gold's claim, and therefore I did not deal with this aspect either. There is a limit to stupidity, even for a primitive believer like me. And even if I may be a complete fool (after all, we do not know each other), do I not also deserve the protection of the principle of grace? Is Davidsonian grace biased only towards atheists and not towards believers? (It is true that at least in this way there is no doubt that the debate will end with the correct conclusion).
The meaning of the parable of the drunkard: between predetermined and predetermined outcomes
Unfortunately, I don't remember the source of Gold's example now, as far as I remember Dawkins brings it up in one of his books (I'll try to look it up again. It was a long time ago). In any case, as I wrote, his goal is to show that there are processes that seem random and yet their outcome is predetermined due to external factors (circumstances) that precipitate/accelerate them. Dawkins uses this to attack the premise of the physico-theological argument for the existence of God. It may seem like a silly argument, and as I will see in a moment it acts as an anti-atheist boomerang, but it recurs quite a bit in atheistic scriptures, and in my opinion it actually demonstrates the fallacy of the physico-theological argument well, which is why I chose this particular passage to address it.
You "translated" this example into a random walk, what you called the impoverished gambler phenomenon, which has a known (and not dictated) outcome in advance. As a physicist, I prefer to look at it as a random walk rather than a repeated bet, although it is of course the same thing. Suppose there is a lattice, i.e. a discrete collection of points at equal distances from each other along the x-axis (for simplicity, let's say at the complete points on the axis). Some drunk starts from some point on the axis, say x=n (what you called the initial conditions), and wherever he is he has a chance p of swinging to the right and q of swinging to the left (the process is Markovian, i.e. without memory, and we assume that the chances are constant at all points and times). The known result you proved is that no matter where he starts from he will always cross the prime (x=0) at some time (as far as I remember, I'm a bit rusty, at least when p=q time is proportional to n^2).
Your process is completely random, but its own properties (and not external constraints) create a chronicle of a predetermined outcome. Precisely because of this, it is in no way similar to the drunkard parable, which deals with the influence of constraints and catalysts, and therefore your translation, which does Gould a favor, is irrelevant to the discussion. You offer another parable in place of his, which demonstrates a different phenomenon, then analyze your parable and finally criticize my remarks regarding his parable. I think it would be hard to blame me if I said that this methodology seems problematic to me.
Incidentally, it should be noted that even in your translation the result (that at least one drunk will reach x=0) is not guaranteed by the data except when enough time passes (n^2) and/or when enough drunks set out. In order to see such a model as an alternative to the existence of an intelligent agent, it must be shown that these conditions are indeed met (that there are enough drunks and/or that enough time has passed). I will note that various calculations that have been made claim that they do not hold (regarding abiogenesis, even Dawkins argues in favor of the "successful case" thesis, and deRob and many others reject it based on the calculation of the number of attempts and time scales. See also the notes at the end), but that is not our topic.
I will add another clarification to the claim made by the drunken government. When I searched for the source of the matter (and unfortunately I did not find it, I do not have all of Dawkins' books at home), I found a very similar parable in the book The Blind Watchmaker on page 61 onwards, in which Dawkins refers to the formation of a significant sentence through a random process of keystrokes on a keyboard (as a monkey dances on it). It is said that we want to create the sentence "I think it is similar to a rabbit" (in the original experiment that I dealt with in the article in Wient, it was the sentence: to be and to be) by random keystrokes on the keyboard. This is software with a random character generator and not a jumping monkey, of course. There are 21 characters here, and if we assume that Hebrew has 27 letters (with the endings) and another space, because then there are 28 possibilities for each keystroke, the chance of getting the entire sentence is 28^(-21). This is something like 1 divided by a number with thirty zeros, which means it is really negligible. Therefore, the time it will take to reach the "correct" combination is enormous (depending, of course, on the monkey's tapping, drawing, or jumping rate). That's about the drawing in a single step. But what will happen in the process he calls "cumulative selection"? This is a process in which the string creates many "offspring" and from them we choose the one that is most similar to the desired string (!), no matter how faint the similarity is. [I didn't see any details there about how many offspring are created at each step]. Surprisingly, Dawkins tells us, in such an experiment the goal is reached after several dozen "generations" (in the 50th or 70th generation). As far as I remember, in the computerized experiment of Being and Beingness they did something a little different: every time they got a correct character in the correct place in the string, they froze it and only drew everything else. And lo and behold, the process there was also shortened by a great deal.
Dawkins' conclusion (p. 65): There is therefore a great difference between cumulative selection (in which every improvement, however small, serves as a basis for future construction) and single-stage selection (in which every new "trial" starts from scratch). If evolutionary progress had to rely on single-stage selection, it would never have gotten anywhere. But if there were some way in which the blind forces of nature could have established the necessary conditions for cumulative selection, then the results would be strange and wonderful. In fact, that is exactly what has happened in our world, and we ourselves are among the most recent, if not the strangest or most wonderful, of these results.
That is, he is talking about a non-Markovian process (which has a memory. Each step in the lottery remembers the previous results and depends on them). In fact, he not only remembers the past but also knows the future (what the goal is, since within the process he returns and compares it to it). This is in complete contrast to the example of the random walk that you brought.
Note that his parable is about an outcome dictated by external constraints and 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 happened and know where they are headed, and thus dictate the outcome and hasten its arrival. There is an external factor here, if you will – the programmer, whose intervention alone brings this “random walk” to the desired outcome. After all, you have our own maligned drunkard parable, in which the wall brings the random drunkard to the desired destination. Is it also right to interpret Dawkins’s words in a benevolent manner and change his parable to something Markovian without constraints and without memory?
My argument is that a proverb like the drunkard's is very common in these discussions, and therefore it doesn't really matter what exactly Gold said. Hence, there is no basis for your assessment that he could not have said it, and even less for the generous "translation" you offered him. In any case, my words criticize the argument that deals with the influence of circumstances and constraints on a random walk, and not an argument like yours that deals with known probabilistic outcomes of a random walk. For my part, this is a criticism of Dawkins and not of Gold (see also the notes at the end).
The conclusions from a process whose outcomes are predetermined
So, we are back to discussing a parable whose outcomes are dictated in advance by external constraints (and not just known in advance as in a random walk). I doubt if I need to explain to readers, and certainly to you, the theological significance of Dawkins' example. What he demonstrates is that while the evolutionary process is not probabilistically possible, if we add a guiding hand (teleological, i.e., outcome-directed, in a blatant way), that is, a programmer who ensures that the computer lottery reaches our desired destination, it becomes something possible. Reminds me of the parable of the drunkard? Absolutely. Even the drunkard cannot reach any goal by random walk, but if we create circumstances around him (a ditch and a wall) that ensure that he will arrive – he will indeed arrive. For example, a random lottery of a "successful" protein chain is unlikely, but when it is broken down into cumulative steps, that is, when there are "external" factors directing it along the way (natural selection, heredity, etc.), it becomes likely.
These metaphors are used by Dawkins in his attempt to refute the physico-theological argument, but in fact this is exactly the physico-theological argument: Noah claims that for an improbable process to succeed, a guiding hand is required, and these metaphors only strengthen this argument and do not refute it. And in the parable, for the evolutionary process to occur with reasonable probability, there must be a guiding hand that determines the rules of the game so that the result is obtained. With other rules of the game or no rules of the game at all, this probably would not have happened. The physico-theological argument claims that this guiding hand is God (for the sake of discussion, we can say that this is actually a definition of Him, not an argument about Him).
Note that Dawkins' and Gould's parables are not based on the fact that there are many repeated attempts, as you put it. It is about the influence of a guiding hand, laws or circumstances, that affects the process from the outside. The focus of the discussion is what are these external "circumstances"? Who created them? Neo-Darwinists 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, thus directing it to its goal and making the assumption of an intelligent agent redundant). The random process takes place within them and under their influence, and therefore it can reach its goal. This is the scientific explanation, and I completely accept it. But my question is on the theological-philosophical, extra-scientific level: 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 (via the wall and the ditch) to his goal. If there were no wall and channel (in Gold) 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, Gold and Dawkins themselves introduced external elements into the system with their own hands so that randomness would lead to the desired result. With Dawkins, it is even more blatant, since he introduces the desired result itself into the process (by comparing it at each stage to the desired string). This is truly an "own goal," since he describes evolution as something directed at a goal that was previously planned so that it would reach it. 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 an emotional prayer to help him. In his distress, he promises Him that from now on he will devote his life only to Torah and Mitzvot. And behold, a parking space becomes available right next to him. Our friend is not confused, and immediately returns to God: "No need, thank you, I've already arranged it."]
Let us now return to the parable. Evolution is a description of a process that takes place within the laws (= the wall and the ditch) and they are the ones who ensure that it "succeeds." Without them, it would not have happened. Now I ask about the laws themselves, where they came from. The physico-theological argument concludes that it is likely that there is a guiding hand that guides the evolutionary process to its goal. So why is it surprising that it actually gets there? These parables are not a refutation of this argument, but rather an excellent demonstration of the thesis that an external intelligent factor is needed to guide the process to its goal (which will provide the gradient of the improbable mountain slope).
If you insist on saying that the laws were created by themselves or that they always were and their nature was determined arbitrarily, that's perfectly fine with me. In that case, the physico-theological argument really won't convince you (any logical argument appeals only to those who accept its premises). But note that you assume in advance that something special (=the laws) can be created blindly. So, what has the evolutionary chatter added to us? If you assume that special phenomena do not require a guiding hand, then of course you don't accept the physico-theological argument (that complex phenomena indicate the existence of a guiding intelligent agent). And if you assume that it is improbable, then you do accept it. Either way, evolution is irrelevant to the discussion, and the arguments of the drunkard or the monkeys and keyboards are even less so.
A few final notes
A. Of course, the discussion is not over. Can we now discuss whether life is indeed "special" in some sense, or whether we marked the goal after it was created? Can we also discuss whether the laws are special? Dawkins discusses this further in his remarks in The Blind Watchmaker, and in my opinion he is wrong there too, and in a big way. We can also discuss whether the thesis of an intelligent agent solves the problem, and whether this term even has any meaning. I dealt with some of these things in my series of articles in Wyant. But all of this already goes beyond the discussion of the passage in question here. Here I wanted to explain what I meant in this specific passage and clarify why your criticism does not deal with my words. For the continuation of the discussion, I can only refer the reader to my article in Wyant and to reading the book.
B. As far as I know, Gold is also an atheist, but he disagrees with Dawkins in a difficult (sometimes very heated) dispute about the status of God in terms of evolution. Dawkins claims that evolution proves (almost certainly) that he does not exist, while Gold believes that the questions are independent of each other (perhaps evolution makes the claim about his existence redundant but does not prove anything about it). I also believe that the questions are independent, since as I showed above, the debate depends on the starting point (can a complex thing be created/exist without a determined intelligent agent), and evolution neither adds nor subtracts to this issue. I explained this above. What I added about strengthening the physical-theological evidence is that if the starting point is that it is unlikely that a complex thing could exist without an intelligent agent creating it (which is what this argument assumes), then evolution strengthens the physical-theological argument. Of course, those who disagree with this assumption will not accept the conclusion, with or without evolution, and that is perfectly fine, at least in terms of logical validity (although in my opinion the assumption is a bit irrational). Therefore, evolution is not relevant to the discussion in any case. Things are made clearer in the book itself. My argument is mainly with Dawkins, and for me the parable that Gold brought is not important (although it is inaccurate). What concerns me here is mainly the use that Dawkins makes of it to attack the thesis of the existence of God.
C. Of course, this entire discussion is about one drunkard, and as you rightly noted, in the evolutionary process there are a lot of drunkards. Note that in Dawkins' parable about the desired string, this has already been taken into account, since there are many lotteries being made there, not just one. But as I explained, the parable of the drunkard is not about this effect, but about the situation that has arisen after we have already taken it into account. In other words, his argument is about a situation in which even if there are a lot of drunkards, the probability that one of them will end up in the ditch is still small, unless there is a wall that takes care of this. Therefore, the parable of the drunkard ignores the number of drunkards, and therefore I ignored it too (although I did add a brief discussion about a paper wall with hard points that alludes to this aspect).
By the way, my book contains a calculation by DeRob that shows this also in the evolutionary context (actually in the context of abiogenesis, meaning that even if we take into account the large number of attempts that were made, the probability of a "successful" chain forming is zero. He has a rough estimate there of how many attempts were made), and the question is addressed there in detail and in detail. So don't worry, I know very well that statistics are not made on a single case, and I'm sure that Gold and Dawkins know this too.
D. It is important now that this response was long (only hypothetical, of course), and in Wyant they would have quoted only the seventh paragraph from it, to demonstrate what it is about. Was there room to criticize what was said in that paragraph as if it were an article that claims something? That is essentially what you did in your post. But, as mentioned, my argument here is that your criticism does not hold water even from within it, that is, even without going into the entire book and the context. In my brief response on the website, I stated that the problem is both that you have not read the book and because of considerations concerning this section itself (the mixing of a discussion outside the laws with a discussion within the laws and an overly generous interpretation of the parable).
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Asks (Gadi Alexandrovich):
With your permission, I think it's better to focus the discussion. My experience is that extremely long responses go far beyond the scope of the discussion and there is no reasonable way to address them.
So to the point: I'm surprised to discover that you brought up an argument that you attribute to Gold and attacked it without actually reading the argument or even having a reference to it. That's not really relevant because then it's not at all certain that you understood what Gold was trying to say through the parable (if at all).
In my post I say "Gould (of this I am absolutely certain) thinks of the drunkard at the very least as a population of some kind."
Here are some 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 about the drunkard within a single organism?
3) How do *you* understand the parable of the drunkard in your text? To whom does the drunkard correspond in your case? A single organism? A population? The entire process? What is the meaning of the canal, and what is the meaning of the "paper wall" in your case?
4) You say "In the evolutionary process we don't have a wall that ensures that the drunkard gets back on track every time." Why is that important? As I explain in the post, the wall is 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 eventually fall into the ditch (regardless of whether there is a wall or not), and if there is a bias in favor of walking away from the ditch, it is not guaranteed that the drunkard will eventually fall into the ditch (regardless of whether there is a wall or not).
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Rabbi:
Hello Gadi. With your permission, I will skip the reprimands and counter-reprimands.
A. I completely agree that Gold is talking about population. After all, that is exactly what I wrote (which, for the sake of discussion, can be said to include the effect of the number of drunks in the model).
B. You are getting into unnecessary grammar. The parable is meant to say that sometimes external constraints accelerate the random process and focus it (moderate the slope of the improbable mountain, as Dawkins puts it). This is also the case with Dawkins' theory of jumping monkeys.
C. The rest of your comments deal with your model, and as I explained, it is irrelevant to the discussion, and it is not for nothing that neither Dawkins nor Gold (probably) nor even I, the little one, deal with it. I must say that in doing so you are repeating the same methodological deception that I discussed at length in my remarks (you probably should have read them anyway), and therefore I will not enter into a discussion about it.
D. In my parable, there is clearly a difference between the model without the wall and with the wall. I think that simple probability calculations will be agreed upon by both of us, and there is no point in getting into quizzes about them.
E. Now I will explain again why your model is irrelevant to the discussion. A random walk as you described (without constraints) is an empty mathematical model. It has no component related to the laws of nature (=external constraints), and its result is known in advance from probability calculations only (and does not really depend on the values of the parameters, as you correctly showed). Hence, there is no representation there for the influence of any laws of nature. If we assume that your model models evolution – it follows that evolution is a branch of mathematics and not of empirical science, and this is of course nonsense. I suppose we will agree that in a world with other laws of nature none of this would have happened.
Therefore, the drunkard model, similar to what I described (and it really doesn't matter to me if you change something in it one way or another), as well as the jumping monkey model (by Dawkins) are indeed the correct models for evolution (except for the corrections I mentioned in my remarks, but it is clearly not about cleaning up the environmental constraints as you suggested). The external constraints in these models (the wall and the programmer) do affect the outcome, and necessarily, express the influence of the laws of nature within which the random process operates.
But as I argued, this is precisely why these models demonstrate well why the evolutionary picture does not exempt us from the conclusion about the existence of a guiding hand (unless we accept that complexity can arise on its own, in which case evolution is again irrelevant to the discussion).
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Asks (Gadi Alexandrovich):
Let's focus more.
If you agree that "Gould is talking about population," I want to understand, before the discussion can continue, why you wrote, "The main problem is that the wall along which the drunkard is advancing is made of paper. Furthermore, behind this wall there is an abyss from which no one who enters will return. Any move towards the evolutionary non-relic (i.e. towards the wall) leads to a dead end of the process, i.e. to the extinction of the creature or its evolutionary descendants."
1) "The extinction of the creature" – what creature is this, if it is an entire population?
2) If you are indeed thinking about an entire population, what does the wallpaper analogy represent? Is it meant to describe an evolutionary change that causes the extinction of an entire population?
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Rabbi:
Indeed. If we do not take into account the "external accelerators" (= the wall), the entire population (= the gene) is doomed to extinction. Dead end in the evolutionary process does not refer to a single creature but to a population or species (= the gene). Evolutionary development eliminates most creatures and leaves behind the strongest ones (the survivors). But even the survivors survive only thanks to the wall (= the laws of nature), and without it they would all have reached a dead end. Just as Dawkins explains that the slope of the mountain is improbable (before the recession). He does not mean a single creature climbing the mountain but a gene.
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Asks (Gadi Alexandrovich):
You contradict 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 then say, "We'll add to our model the fact that there are a tiny number of dots on the wall that are made of hard stone, and hitting them will send the drunk 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 ray of the dilemma? Regarding your words: First, at the level of the genotype. If you look at the collection of all protein chains, there are such masses (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 essentially a random walk between them, that is, a hopping between these islands. The jump should take us from one living island to another living island. A missed jump is a dead end. Because these islands are so rare, this would not happen in any way in a normal random walk (without constraints) if there were not laws of nature (a wall) that ensure that this happens, meaning that there would be a reasonable number (still small, but enough for the gene to survive) of jumps in the ocean from the island on which they are located to other "living" islands. These laws transform a wall from a paper wall (with a few stiff spots) into a stiff wall, or alternatively ensure that a sufficient number of jumps will damage its stiff spots. Here is an example on the phenotype level. Consider the case of the origin of the porcupine. There was a drought on the island and all their food plants became extinct. Only plants remained whose hatching required an especially strong beak, and thus the porcupines with the strong beaks survived, passing this trait on to their offspring. It could have been a situation where all the plants would have become extinct, or there would have been no birds with strong beaks, because the mutations in the porcupine would have created a crippled elephant or simply a structure whose phenotype is not that of a living creature (a three-winged fairy). Alternatively, if there were no laws of heredity, this trait, although selected in the natural process, would not have been passed on to the offspring, and the porcupines would have become extinct. The laws of evolution (mutation formation + selection + genetics) moderate the slope of the improbable mountain and ensure that the mutations also produce something close, such as a parrot with a strong beak, and/or that not all plants always become extinct. This is how the parrot's gene survives and is passed on to the next generation. If there was a purely random process here (without the accelerating influence of the laws of nature), it is unlikely that this could have happened.
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Asks (Gadi Alexandrovich):
I understand (I don't agree, but at least I understand).
Your claim is that Gold claimed that this was a completely random move? Prove it.
Well, I decided that I'd better do the research that hasn't been done here so far. Gould's use of the parable comes from his book "Full House: The Spread of Excellence from Plato to Darwin." I'll quote the relevant part in its entirety. Am;lak: As I thought, Gould is not trying to claim in any way that the drunkard's parable describes evolution at all. He presents it as a simple mathematical example of how, in a random process (one where there is a 50:50 probability in either direction), a preference for a particular direction (the canal) arises.
I think he is wrong in his interpretation. He brings up the wall as the reason for the creation of the preference. As far as I understand, the wall is not related at all and could have been dispensed with; the reason why a "preference" is created is that once you reach the canal - that's it, you are stuck there. If there were no canal, the process would reach arbitrarily large distances on both sides and be eliminated. In other words, I think Gold is using an incorrect mathematical metaphor here, although with a more careful mathematical analysis of the drunkard's situation with the wall, perhaps something consistent with what he wanted to say could be achieved.
If so, what was done in the Ynet article is obviously dishonest. The article attacks the parable as if the parable was meant to describe evolution. According to Gold, explicitly, the parable is not meant to do that but to clarify a more fundamental point.
(I personally think that any attempt to describe evolution using this parable is completely ridiculous, which explains the stupid discussion 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 variation by a single "thing" or entity interpreted 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 barely 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 the 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 to an appropriate account for the entire history of life. Since we can approach these largely unknown plankters without the strong biases that cloud 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 a 50 percent probability. The bar wall on 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 irreversible 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 in 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 as 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 whatsoever, 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 whatsoever towards 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 started with the fact that I understand nothing about evolution, mathematics, and in general I talk nonsense. Now I have the impression that we are in a slightly different situation. I will try to explain the situation again according to my understanding. If you would like to continue the discussion (the stupid one, also by your definition, which I completely agree with), please tell me what your original claim in your post was about. I would appreciate it if you would not raise new claims at this point, but simply explain what you meant when you said that I understand nothing and talk nonsense (within the context of the section published in Wyant). After that, we can discuss additional things if you wish. 1. Background to my claim: Evolution is actually a type of random process that, in a simple probabilistic calculation (=outside the laws), has almost no chance of coming true. The fact that it does come true is explained by the fact that this random process happens within the framework of external constraints (=within the laws. The laws of nature: biology – including physics and chemistry, genetics, the ways in which mutations form, etc.). In this way, evolution is part of the natural sciences and not mathematics. My basic argument in the book is that if there are external constraints that only caused us to get this far in a blind and random process, it is reasonable to assume that there is an intelligent agent who created them and thus actually caused this result. As mentioned, this argument is not necessary but very plausible (in my opinion). Anyone who is willing to accept complex things without an intelligent agent will of course reject the conclusion. But any logical argument appeals to those who adopt its assumptions (very plausible in this case, in my humble opinion). 2. So much for the background, and now for the passage in question published in Wyant. I remind you – your words were only about it (since the background was probably not familiar to you at all): A. I brought up the parable of the drunkard there and claimed that it came to express the idea that a random process can reach its goal with the help of external catalysts/constraints. A claim that Gould himself makes in the passage you brought, and also Dawkins in countless places. These catalysts are essentially the aforementioned laws of nature. In my words to you on my website, I added Dawkins' parable about the accidental creation of a string of characters, which says exactly the same thing in principle. B. I then argued that these parables do indeed correctly describe evolution (see background in section 1), but they do not refute the physico-theological argument about God, but rather demonstrate its logic well (for those who accept its assumptions, as stated above). They show that in order for a random process to reach a complex result, a deliberate hand is required. That is more or less what I wrote there. 3. Now to your post: You claimed to me in general that my words in this section (i.e. the last paragraphs a-b above. You did not know the background at all) are a mathematical misunderstanding, that I know nothing about evolution, and that I am talking nonsense. I think that is a fair summary, even if I have summarized something, of your words to me. In addition, you offered another explanation, fictional Something, like Gold's parable, which you now also agree is not really what it says there. You also agree that Gold was wrong exactly in what you (mistakenly) attributed to me, in saying that the wall affects the outcome. In the parable as I understood it, it does indeed affect. 4. So what's left of all this? Right now, it seems that all we have to do is interpret Gold's scriptures, and find out whether Gold said the parable exactly this way or that way. This doesn't really touch on the body of my arguments, and certainly doesn't indicate a mathematical or scientific misunderstanding as you attributed to me. Therefore, it doesn't touch in any way on the main point of your post. But if for some reason you still want to know my opinion on Gold's words, which, as I said, is really unimportant to me, I still stand by everything I wrote about them. Gold does describe the idea of evolution in this parable (as he writes here in the commentary), he shows through it that external constraints can focus a random process, and of course he also includes the wall (which, according to you, has no effect). Therefore, to your question In the last message in this thread, in my opinion, he is not dealing with random movement. Now I will just add that if he, as an atheist, assumes that there is no deliberate hand, then in my opinion his words are really implausible. I can only agree that the discussion here seems a bit critical and stupid, as you wrote, because from all the great ideas and strong accusations we have come to clarify the position of that righteous man (Gold). But I think that is not really my fault. 5. And another reminder: I cannot help but mention again the methodological problem that I pointed out in my long response, and also your statement about a contradiction between one of my statements (that the wall is made of paper) and… until now I don't 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 a single hand clap make?). 6. And finally: Now that you understand what I meant (even if you don't agree, which is perfectly fine for me), I would be happy and appreciate it if you would see fit to insert a correction or an apology. Any comments about the heated and unfounded post, which is very uncharacteristic of you. This is precisely because I greatly appreciate your writing and probably others do too. Even if you don't find it appropriate to do so – no problem. We can part as friends after our brief friendship here. It was nice to meet you.
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Asks (Gadi Alexandrovich):
1. This background is clear. I think it is misleading to the readers because it is impossible to define anything "outside the rules", although I would love to see you *formally* define a random process *for evolution* that is *outside the rules* so that a "simple probabilistic analysis" of the type you describe can be performed on it. This background is not included in the article that appears on Ynet and is therefore not really relevant to the review.
2.
A. That's not what Gold says, but let's leave it at that.
B. That's not what you do in the article. In the article you take the parable, which Gold does not even try to claim describes evolution, and say that it is *wrong* ("The problem with this parable lies on two different levels...", "Gold's absurd model"
).
Here you commit, in my opinion, a serious deception of the reader. You take a toy that no one claims to describe evolution, dismiss it (and therefore Godel) as an incorrect description of evolution, and then use the same toy, with slight variations, to describe evolution. This is ridiculous. You are using a completely ridiculous and simplistic model to talk about evolution.
I don't know if you meant it that way, but it seems like you're trying to make the reader think that if Gould used this model to describe evolution, then it's okay to talk about evolution using this model, and you just need to make a few corrections (for example, your paper wall). After all, Gould is one of the "good ones." This is a serious deception of the readers and I really hope that's not what you meant; but if that's not what you meant, it's great that I understand why you're talking about this model here in the first place. Gould brought it up to make a *very specific* claim that you don't contradict or even talk about at all.
3. What I am saying is, "I can say about this argument – either I don't understand anything about evolution, or Rabbi Dr. Avraham doesn't understand anything about evolution (or we both don't understand anything about it)." That is, I don't really pretend to say anything about Rabbi Dr. Michael Avraham, 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 to Gould is fictional, because I was mistaken at the time in thinking that Gould was indeed trying to use the drunkard parable to describe evolution. I accuse your article of this deception. If you wish, I can amend my post to absolve Gould of the charge of trying to use the drunkard parable as an evolutionary model and explain that this is a deception that your article is committing.
Now, I assume you want to say that the passages I mock in my article are not as stupid as I present them. They may be. But for that you would have to explain in detail their meaning and how it arises from the text; not offer other ideas that appear in yours elsewhere and contradict your text. The text says, for example, "In the evolutionary process we do not have a wall that takes care that every time the drunkard gets back on track." 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 suggest: Want to save the article? Take the three paragraphs I quoted, and write an explanation for them. The explanation should include: the exact mathematical model you use to describe evolution; the aspects of evolution that fit the mathematical model; the meaning of any ambiguous words in your text, and so on. Then we can de-index.
For example, what is an "evolutionary step"? Is it a single mutation that occurs in a single individual in the group? If so, why does such a step, if it leads to the creation of a "non-living mutation," halt the evolutionary process at the group level? (It doesn't). If not, how common is it? Do these probabilities match the probabilities in the mathematical model of the drunk, in which the probability of going towards the wall is the same as the probability of going the other way? Etc., etc.
4. As I've tried to say here several times, I'm not really interested in Gold, and my post isn't really trying to defend him. However, I think the interesting part of the whole story is that it turned out to me here that you didn't even read Gold's text before writing the article.
5. The contradiction is between the description of the wall as something capable of returning those who hit it, and the description of the wall as being made of paper and anyone who crosses it is destroyed. Later in your article you change this model to a wall with "a tiny number of dots on the wall that are made of hard stone" and this resolves the contradiction (i.e., replaces the conflicting models with a unified model), but to see this I had to bother rereading the article.
This highlights what bothers me about your writing: you start unnecessarily with incorrect models, without even hinting that they are incorrect, and after a long engagement with them that is not really helpful, you quickly move on to talking about the less incorrect models. Another problem is that even the less incorrect model does not necessarily correspond to 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 to clarify that your article misled me into thinking that Gould was actually trying to provide an evolutionary model with the drunkard's parable, when in fact he is not.
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Rabbi:
Hello Gadi. Unfortunately, you are escaping into foreign and irrelevant realms, which is a shame. Things I have already explained well, you repeat and explain, you demand an explanation for them once again. You demand a calculation where no calculation is required to understand the claim, and you send me to write a Rashi commentary and Tosafot on my words and Gold's words, even though you think they are wrong (and I don't think they are) and even though you admitted that your understanding of them was also wrong (although in a strange kind of rhetoric I am the only one guilty of this). I repeat for the umpteenth time that these models do not come to describe evolution in its entirety, but rather the idea of evolution, which is: that external constraints accelerate or improve the focus of a random process and the likelihood of achieving a "successful" outcome. This is the main idea of evolution, and there is no argument between Gold and Dawkins and anyone else who understands it. Almost all of Dawkins' books are devoted to this, as well as some of Gold's works, and this is well demonstrated by the model. For my purposes, this is completely sufficient. 1. Of course it is possible, and it is even very easy, and I have already done it here more than once. If you had not insisted, I am sure you would have seen it yourself. For example, Your random walk model is "outside the rules" in this sense because it has no empirical input whatsoever (at least regarding the results that do not depend on the parameter values). Similarly, drawing a single chain from all theoretical possibilities (not just the "animal" ones) is a model outside the rules. The rules focus you more in the direction of the "animals". The drunk without a wall and the blind typing without the help of a programmer are outside the rules. I have defined this over and over again, and you insist on ignoring it. But indeed, none of this is related to our discussion in this section. 2. I repeat for the umpteenth time: On the contrary, this model well describes the idea of evolution (a random process that undergoes acceleration, or a gradient slowdown, by circumstances and constraints). It is true that you will not find in the canal what expresses the cut-tailed grasshopper or the three-tailed grasshopper, since there is no model here for all evolution but for its fundamental idea. This is the essence of Gould's and Dawkins' description For evolution. I wrote that it is wrong only as a model that comes to explain why evolution is an explanation that stands on its own (without the need for an external factor). 3. It seems to me that you are really being dishonest here. Ask the average reader how he understands this sentence of yours. In addition, see also your less polite and less indirect words in the talkbacks. But it seems again that you are a fan of Tos' commentaries over Rashi's commentaries (= the simple meaning of the texts in question). By the way, I completely agree with the claim you quoted here: "About this argument I can say – either I don't understand anything about evolution, or Rabbi Dr. Avraham doesn't understand anything about evolution (or neither of us understand anything about it)." The correctness of my argument entails one of the components of the disjunction in the Sipa (although I assume we disagree about which one). As a mathematician, you certainly know that if Q exists, it also implies "Q or P." Since you repeatedly repeat the methodological distortion I pointed out, criticizing this chapter as if it were an article that obviates the need for context, I suppose you'll forgive me if I don't enter into this stupid discussion (as you yourself defined it). You expect such a text to present probability calculations in a popular text, and this is when the facts (which are an improbable slope, if we don't take into account the recession of the laws of nature) are agreed upon by everyone, including Dawkins and Gould and anyone who is even slightly familiar with the matter. The sentence you quoted says that in the evolutionary process according to Dawkins and Gold (!) we have no wall, since they (as atheists) claim that a full explanation of the phenomenon of life did not include any additional factor beyond the evolutionary explanation. The debate is about that and not about the correct model for evolution. We all agree on this (except for you, apparently). But to understand this, you need to see the context, which you did not do. 4. Indeed, I did not read Gold just as you did not read my words before criticizing them. The difference is that I only needed the principle (and therefore there is no need to verify details, and there is no problem using a secondary source, especially from an expert like Dawkins) and I was right, while you criticized the details (and therefore you should have read the context, since this is not an article but a demonstration piece) and you were wrong. I have nothing to comment on 5-6.