Probability and Statistics – Lecture 22
This transcript was produced automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
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Table of Contents
- Lot, lottery, and fairness
- Ad hoc lottery and Bible codes
- Rarity versus specialness and inference from probability
- Ad hoc on the ship, consent, and basic fairness
- Eli Merzbach, providence through randomness, and the meaning of fairness in lotteries
- Statistics, determinism, and the claim of “involvement within nature”
- Prayer, blessings, and the distinction between acting and asking for a miracle
- Miracles, falsifiability, and the law of small numbers
Summary
General Overview
The speaker distinguishes between a lot and a lottery according to purpose: a lot is meant to receive an answer from the Holy One, blessed be He, and therefore in his view fairness of odds is not important, whereas a lottery is meant to distribute chances equally within a world of natural chance, and so fairness is essential. He completes the discussion through the example of “Bible codes” in order to show how an “ad hoc lottery” is created when one chooses the search mechanism or lottery mechanism so that it yields a desired result, and he connects this to the fallacy of inferring God’s hand from a rare event without fixing in advance what counts as a special result. Later he attacks Eli Merzbach’s thesis that randomness is the hidden mode of divine governance of the world, and argues that divine involvement means a deviation from the laws of nature, not action “within” the laws of nature. From this it follows that inferring “hidden miracles” from low-probability events requires statistical examination that people generally do not perform.
Lot, lottery, and fairness
The speaker states that the difference between lots and lotteries depends on the purpose for which they are used, and from that it follows that fairness of odds is not a central condition in a lot. He argues that in a lot the Holy One, blessed be He, determines the outcome, so it does not matter what the probability is, whereas in a lottery the outcome is random “in the ordinary course of the world,” and therefore fairness matters in order to distribute chances equally among all participants. He places at the basis of the distinction the question whether the Holy One, blessed be He, is involved in determining the outcome, and defines a lot as a case of involvement and a lottery as a natural case.
Ad hoc lottery and Bible codes
The speaker brings up the dispute over “skips or Bible codes” as a thesis according to which one can find encrypted information through equidistant skips, and notes an article by Doron Witztum and Eliyahu Rips, as well as a committee at the Hebrew University in which Aumann and Furstenberg participated, that moved between accepting the possibility and returning to a noncommittal position. He describes delays and ideological debate surrounding publication of an article in a statistics journal, and recounts that he was sent to hear Witztum at a conference in Givatayim on behalf of Netivot Olam Yeshiva in Bnei Brak, and returned without a firm conclusion but with suspicion. He presents criticism by Maya Bar-Hillel, who applied similar algorithms to other books and argued that “findings” can be found there too, and mentions opposition by Barry Simon.
The speaker explains that a common claim against the codes is that results are found only after the event has already happened, but he weakens this with the technical point that before the murder there is no “name” to search for. He sharpens a more serious claim, namely that the code “comes after the information and not before it,” because people play with parameters such as “minimum skip” and with different percentages of the text until they get an interesting proximity, and thus in practice choose the mechanism that will yield the result. He argues that if one can choose the code מתוך many possible codes, then the correct probability question is “what is the probability that there will be some code that gives this result,” and the answer is that usually one can always build a code that gives the desired result in any book. He compares this to Wittgenstein’s argument about rule-following, according to which one can always fit a formula to a sequence so that the next term will be whatever one wants.
Rarity versus specialness and inference from probability
The speaker argues that an event with low probability does not necessarily call for explanation, because in many experiments every concrete result is rare in advance. He illustrates this with many coin tosses, where every sequence has a tiny probability, and yet some sequence must occur, so rarity itself is not evidence. He distinguishes between a rare result and a special result, and argues that a sequence like “six six six…” in rolling a die becomes suspicious because it is marked in advance as a special result and not merely because of its rarity.
The speaker tells a story about his sister meeting, at a summer camp in Canada, a young man from Jerusalem, and shows that the wonder does not stem from the fact that the probability of a certain origin is low, but from the fact that “Jerusalem” is a marked and special result for her. He applies this to Bible codes and argues that finding patterns around a number chosen in advance as special, such as seven, is more meaningful than matches around a random number chosen only after the fact.
Ad hoc on the ship, consent, and basic fairness
The speaker connects the problem of Bible codes to the problem of “the lottery on the ship from Liverpool,” and argues that when one chooses the manner of the lottery in order to guarantee a desired outcome, this is not a fair lottery but choosing an outcome under the guise of a lottery. He explains that one could always choose a different criterion that would reverse the outcome, and therefore the problem is the choice of mechanism, not the equality within the chosen mechanism.
In response to a student’s question about “might makes right,” the speaker distinguishes between fairness that stems from a fair mechanism and a situation in which it is “fair because everyone agreed,” and argues that a person can agree to an unfair mechanism and still have no claim afterward once he agreed. He adds that in Sodom the agreement was imposed on guests who were not parties to the agreement, and therefore it is not fairness.
Eli Merzbach, providence through randomness, and the meaning of fairness in lotteries
The speaker presents Eli Merzbach’s claim that randomness in the world is the way the Holy One, blessed be He, hides Himself and governs the world, and therefore the lottery is a hidden mechanism of governance. He argues that if so, there is no difference between a lot and a lottery and everything is “in God’s hands,” and from this the importance of fair odds collapses even in practical lotteries such as dividing an inheritance by means of a coin. He gives an analogy of an urn with ninety-nine red balls and one black ball, and argues that if there is an agent who in practice chooses according to his will, then the odds ratio does not constrain him.
The speaker accepts a remark that this claim also has implications for the claims of a thief or murderer, “if God had not wanted it, I would not have succeeded,” and stresses that it is the same logic. He argues that the demands of halakhic decisors for a fair lottery, to the point of saying that “the results are void” when the lottery is unfair, do not fit with a view according to which the Holy One, blessed be He, decides the outcome of the lottery in any case, and he notes that Chavot Yair even required fairness in a lot as well.
Statistics, determinism, and the claim of “involvement within nature”
The speaker formulates the fundamental question of the Holy One, blessed be He’s involvement in the world through the concepts of doubt and statistics, and argues that speaking about statistics in its ordinary sense assumes that the Holy One, blessed be He, does not manage ongoing occurrences. He compares “randomness” in lotteries to “nature” as deterministic laws and argues that in both there is no meaning to divine involvement so long as the result is determined by the mechanism itself.
He argues that if the world is deterministic, then from a given state one result follows according to the laws of nature, and divine involvement means a deviation from the result that should have occurred, that is, a miracle or a suspension of the laws of nature. He states that there is no such thing as “divine involvement within the framework of the laws of nature,” and defines that idea as conceptual confusion, while distinguishing between saying that the Holy One, blessed be He, created the laws of nature or “feeds” their operation, and saying that He changes outcomes within the framework of the law without deviation. He applies the same structure to free choice as well and argues that when a person chooses freely, he changes the natural course.
Prayer, blessings, and the distinction between acting and asking for a miracle
The speaker links the status of prayer to the question of involvement and argues that praying for healing or livelihood means asking for intervention that will change the natural course, not asking that the laws of nature “work.” He says that if he were convinced there is no intervention at all, he would abolish petitionary prayer because it would be mere “moving of the lips,” but he is not completely convinced, and therefore does not abolish it in practice. He argues that in ordinary matters of livelihood and health, “it usually has nothing to do with the Holy One, blessed be He, in any way,” and presents as the proper approach the principle “if there is something you can do, do it; don’t pray,” citing “Why do you cry out to Me? Speak to the children of Israel, that they go forward.”
He brings a Lithuanian story about Rabbi Shlomo Kluger, in which a young rabbi answered a question on the basis of prayer and coming across a book, and Rabbi Shlomo Kluger threw him out and said, “You need to know how to learn, not how to cry,” in order to illustrate a preference for action and learning over dependence on prayer as a problem-solving mechanism.
Miracles, falsifiability, and the law of small numbers
The speaker distinguishes between the a priori possibility of a sporadic miracle and the question whether there is a way to identify a miracle from a particular event, and asks whether this is a theory that can be falsified and whether it can be assessed “even statistically.” He presents Daniel Kahneman’s “law of small numbers” as a fallacy in which one assumes that the statistical behavior of large samples also holds in small samples.
He gives the example of a bullet that stopped in a pocket Psalms book and argues that without examining how many similar cases ended differently and how many happened altogether, one cannot infer a miracle from the apparently low probability. He criticizes “miracle” literature, such as stories about Gush Katif, and argues that no one bothers to compare them to relevant impact data and calculate significance. He explains that even if a rare event occurred, one must ask whether it is special and not merely rare, and compares this to the national lottery, in which the winning of a particular ticket has an infinitesimal probability but does not indicate intentional involvement because one of the tickets had to win.
The speaker is asked what result would be supposed to convince one of divine involvement, and he answers that this is a difficult question, and that where the probability is truly low after relevant examination, he is willing to accept a claim of involvement, but intuitive use of “low probability” as a proof framework is a mistake. He concludes by saying that the continuation of the discussion will deal with additional statistical fallacies and with evaluating cases that seem “unlikely” on the face of it.
Full Transcript
[Rabbi Michael Abraham] Okay, last time we talked about lots and the difference between them and lotteries. We saw that lotteries—that is, the difference between lotteries and lots—depends on the question of what purpose we’re doing it for. But from that difference, other differences follow. For example, with lots, in my opinion at least—even though the halakhic decisors say, many decisors say otherwise—but in my opinion, when we do a lot, not a lottery, fairness isn’t important. After all, the Holy One, blessed be He, determines the outcome anyway, so what difference does the probability make? In lotteries, on the other hand, where my assumption is that the Holy One, blessed be He, is not involved in lotteries and it’s a matter of natural chance, then fairness definitely matters, because I want to distribute the chances equally among all the participants. That’s the whole idea of a lottery. So there, yes, it has to be done fairly. And underlying the whole issue is the question whether the Holy One, blessed be He, is involved or not involved. In lots, the Holy One, blessed be He, is involved and determines the outcome, and in lotteries it’s the ordinary course of the world. So before I continue, I just want to add something, a small completion regarding the previous section when we talked about the lottery on the ship from Liverpool. If you remember, I talked there about the question of that person who threw a few others into the water in order to save himself—why the lottery of genetics is not a legitimate lottery. We talked there about the fact that this was an ad hoc lottery. I just remembered an example that can clarify this better, and I didn’t say it in the lecture, whether that was last time or the time before. There’s a big debate around what’s called the skips or the Bible codes. Right, that thesis that you can find all kinds of hidden information in the Bible if you search for it through some kind of uniform skips or something like that. This whole story came up for discussion a few decades ago—I don’t remember exactly, but something like forty years ago, I think, maybe a bit less. Thirty or forty years. When an article was published—there was also some American journalist who wrote something about it, Michael something, I don’t remember—but in the academic context there was an article published by Doron Witztum and I forgot the name of a Russian mathematician from the Hebrew University, kind of a Chabad guy I think. An article was published about their finding very high significance in skips in the biblical text. You can supposedly find all kinds of encrypted information there. For example, I don’t know, they find the name of Sadat’s murderer adjacent to Sadat’s own name. It’s found in the same place in the Bible when you do the skips, or all kinds of things of that sort, and they argue that there is something special about the biblical text. Some people use this as a kind of proof of its divinity, of its divine origin, because in ordinary texts you don’t find information of this kind. Fine, there were big controversies; it was very interesting. The controversy around it was very interesting, because the feeling was that there was no real willingness to listen to one another. Everyone was dug into his position. Some weren’t willing even to entertain the possibility of such a thing, and the others swore by those skips, and the whole debate was fascinating. There was, yes, Eliyahu Rips, exactly. There was a committee on this on behalf of the Hebrew University that included two religious mathematicians, Aumann and Furstenberg, and at first they argued that it couldn’t be ruled out—that there was something to the claim—and afterwards they retracted and said that actually they didn’t have a clear position, they couldn’t determine whether there was really something there or not. There are even formulations more negative than what I just said. In the end, somehow it came out that there wasn’t—I don’t think there was any very clear statement there. Also in the article that was sent to a statistics journal, that article was held up there for a very long time, I think years. Various referees objected, then supported, and this and that, and there were whole debates until the editorial board decided to publish it with a note—the article. To publish it with some note saying there had been objections and debates, and they were publishing it for the public’s benefit, let the public read and judge. In other words, they did not take a position on the matter. But again, the feeling was that the debate there was an ideological debate, not a professional mathematical one. One of the common claims—because I was once sent to check this matter out when I was in the Netivot Olam yeshiva in Bnei Brak, a yeshiva for ba’alei teshuvah. So they asked me to go—there was some gathering of mathematicians in Givatayim, at one of their houses, and Witztum came there to present this to them. And they asked me from the yeshiva to go hear it, because they wanted to know whether there was really something to it and whether they could use it. They were definitely, let’s say, responsible and honest guys, and they didn’t want to use this thing if it really didn’t hold water. So they sent me as an emissary to check how much… Well, I came back and told them: look, I can’t—it’s not enough. Just sitting there and hearing a lecture isn’t enough to determine a position on this issue. On the face of it, it looked a bit dubious to me, but I can’t state anything clearly. There were some arguments there at the conference too. It was interesting, in short. In any case, one of the claims that comes up in this context—one of the leading fighters is Maya Bar-Hillel, who is the mother of Gili Bar-Hillel, the translator of Harry Potter. She is from the Hebrew University, from the Center for Rationality, and she also wrote against these things. She’s one of the leading opponents of this whole matter. There was—now I’m remembering too—I have lots of anecdotes about this. I remember that another one of the leading opponents from the United States is Barry Simon, the one who wrote the bible of applied mathematics at the University of Chicago, and he himself is an observant Jew. And he really doesn’t believe in this, fights against it, writes against it. He was supposed to come to Israel—he did come to Israel—to talk about it at the Yakar Center in Jerusalem, and I was already in the car to travel from Yeruham, I was already in Yeruham then, and I was already in the car to go, and after five minutes of driving I got a phone call from my wife that she was having contractions. I turned back and didn’t get to hear that lecture. Okay, enough heroic tales. One of the main claims against these codes is that you always find this information after it’s no longer relevant. In other words, we don’t find the murderer of Sadat before the murder, when maybe we could prevent the murder; we always find it after it happened. And therefore of course it raises suspicion that you’re basically tailoring the results according to what you already know. You can’t predict or find results in advance. Now this claim in itself sounds better than it is. It’s not as strong a claim as it sounds. Why? Because think for example about Sadat’s murderer. Before Sadat’s murder happened, I didn’t know whom to look for. I didn’t have a name in my hand, so what exactly am I supposed to search for there in the skips in the Torah? I have no name. Once I have a name, I can search where it appears, if it appears. But if I don’t have a name, then I don’t have whom to search for. What can I do? So there’s a technical problem here that really does prevent us from finding it in advance. So that weakens the point that we always find it afterward, but on the other hand there’s a good explanation for that: you can’t find it beforehand. There’s nothing to be done. But I want to focus on a point related to this, and it bothered me also at that conference in Givatayim. When he was speaking about it there, after all you need to present an algorithm. In other words, what is your algorithm, how do you find the information? You have to give the algorithm in advance and then apply it to the text and see whether you find it or not. By the way, one of the things Maya Bar-Hillel did was apply the same algorithm to other books and show that there too you find all kinds of things. In other words, what he is actually showing us—yes, here’s another anecdote about it. I was the Purim rabbi at Netivot Olam there, in that same yeshiva in Bnei Brak, I was the Purim rabbi. And then I told them that I had found amazing findings in the area of letter skips: I found the word Esther with a skip of exactly one in the Book of Esther. Unbelievable—it can’t be accidental. The Purim rabbi is the Purim clown who says humorous Torah thoughts. So yes, I found the word Esther with a skip of one exactly in the Book of Esther. It’s unbelievable and apparently the hand of God did this, and things of that kind. But what are all these claims actually saying? What they’re actually saying is that you fit the code in order to find the information. The code comes after the information and not before it—that’s really the claim, and that already is a serious claim. In other words, what he showed there regarding, say, Sadat’s murderer and so on—I don’t remember if that was the example, but it’s one of the examples they brought—what he does is search for some word, let’s say, he searches for it in equal skips in the text. So he runs it, say, from the first letter—suppose you want the word Esther—you start in Genesis, aleph, resh, aleph—the first time the letter aleph appears, you look for the next time a samekh appears, then the next time a tav appears, and so on. You see where you find it in equal skips, yes, at the same interval between aleph, samekh, tav and resh, and you find it somewhere that’s supposed to be connected to Esther in some way. Or you want Sadat’s murderer next to Sadat, or something like that. Now when he showed the search algorithm, the algorithm was fairly complicated. It wasn’t straightforward, meaning you don’t just set some algorithm and run with it. Rather, you find it in the minimal skip over seventy percent of the book. Now of course you play with the percentages, and then you arrive at the point where Sadat’s murderer is next to Sadat. And the moment you can play with the code, the results are obviously much less convincing, because you can always play with the code in a way that fits the results so that they look interesting or unique. And again, to test this seriously, it’s not enough to say that he’s playing with the results. You need to say: okay, and what is the probability, even with this playing around, of finding a significant result? And if the probability is very small, then it still means something. But it already raises suspicion that there’s a problem here. It’s not as it is often presented: I’ll tell you in advance what you’ll find, you’ll run it on the text and for sure you’ll find it. No. If you didn’t find it, you tweak the code a little, arrange it until in the end you do find it. Now true, you find it, and it’s not trivial, but it’s also not as unequivocal as it’s usually presented. And therefore in the end I told them that I couldn’t state a clear position on the issue, but I was suspicious. In any case, what lies behind this? Look, let’s try for a moment to think about how this whole thing works.
[Speaker B] Wait, beyond that, first of all it would imply that it’s good that the Holy One, blessed be He, planted the name of Sadat’s murderer, and besides that, what about a hundred other murderers or a thousand other murderers that we didn’t find?
[Rabbi Michael Abraham] You’ll find them too—who says not? You’ll find them too. Search and you’ll find. They claim you find everything. There’s one of them, a mathematician, who was my neighbor in Bnei Brak. He claims he found the date and the missiles that would fall in Bnei Brak, and he found it a day before, against the claims that it’s always afterward. I said it was a shame he didn’t warn us. I was almost his neighbor—he should have warned us. But I believe him, by the way. He wasn’t lying. In other words, there is something here. I don’t think you can dismiss it out of hand. There were very serious mathematicians who support this business. It’s not simple either way. Again, I’m not expressing a clear position here. These simple questions were asked, meaning you’re not going to catch them with these simple questions. In any case, the point I want to convey that concerns us is that any book you take—if you try to find Sadat’s murderer next to Sadat and get them to appear one next to the other—you’ll succeed in arranging a code that does it. There’s no problem. In other words, if you want to find my name in the Book of Genesis, no problem. Take Genesis. Suppose it comes out, I don’t know, ten, fifteen, thirteen, and eight. The intervals between mem and yod and kaf and aleph and lamed—Michael. Okay? Now I can give you a formula that will give those numbers, those fifteen, ten, eight, twenty-one—because I don’t remember the numbers I just said—but something that will give a formula that yields those numbers. If I arrange the code, I can find you whatever you want, anywhere. And it will indeed be special, but the probability of that happening is zero. I can find a code that gives you that result, and the probability that that result would happen is zero, and still it isn’t impressive in any way. Exactly like any result—say you toss a coin, okay? And you write down what came out: one zero one one one zero zero one zero one zero and so on, you write a whole sequence of ones and zeros like that, say a thousand tosses. Okay? Now you made a thousand tosses and wrote down all the numbers. What is the probability that such a sequence would come out? Zero. Or more precisely, two to the minus thousand. That’s a very, very tiny number. You can’t even imagine how tiny it is. It’s a minuscule number. There is no chance that such a thing would happen, and yet here it happened—look, I wrote down what came out, it actually happened. Why? Because there are experiments of this type where every result that happens there is a result with negligible probability, but some result has to happen. Now if I don’t determine in advance what the interesting result is from my standpoint, then it means nothing. In other words, the fact that the result that came out is a result with very small probability—what does that prove? Any result I would have written after a thousand such tosses would have been a result with the same small probability. In the end I know in advance with certainty that a result with very small probability will come out. So the fact that the probability is small says nothing. When can such an experiment say something? Say, finding skips that show that this book was really written by an entity that knows something, or die results showing there’s something special about this die, or this coin, or whatever. When can I infer conclusions from an event whose a priori probability is low? We are used to thinking that if an event happened whose probability is low, then there’s some miracle here, something happened that requires explanation. But that’s not correct. There are many experiments in which whatever happens will have low probability, and I know in advance that something with low probability will happen. In the national lottery, what is the chance that a particular ticket will win? Tiny. But the ticket that did win also had a tiny chance of winning. One of the tickets has to come up in the lottery. So the fact that in the end an event happened whose probability was tiny says nothing. When does such a thing say something? So for that I have another story. My sister was a counselor many years ago at some Jewish summer camp in Canada, near some lake in Canada. On the Sabbath she went for a walk there by the lake. She left the camp and walked there by the lake, and then another person appears there. Unbelievable as it sounds—a guy from Jerusalem. She told me, listen, it’s unbelievable. A guy from Jerusalem of all places shows up there. So I said to her: and if he had come from Tokyo, or I don’t know where, Zimbabwe, or Washington, would that have been less surprising? Is Jerusalem bigger than all those cities? The chance that someone—suppose for argument’s sake he’s uniformly distributed over the whole world—would come from Jerusalem or Tokyo or Zimbabwe… I mean, he has to come from somewhere, and that place he comes from is always by definition one out of millions of possible places, therefore the probability that he’ll come from that place is tiny. So as it happens, he came from Jerusalem. So what? What difference does it make if he had come from Tokyo? Now, that’s not exact. Why isn’t it exact? Because in this case there really is something surprising here. There’s a difference between the probability that someone comes from some place, one over the number of places—suppose for discussion that all places have the same number of people; that brings us back to an available majority, the shop with a large number of pieces and a small number of pieces. So there’s a difference between that and a situation where I mark a result as special in advance. For example, if on a die you get six six six six a thousand times—I rolled a die and got six six six, six. That doesn’t have a lower probability than any other chain of a thousand results. Same probability: six to the minus thousand. So why does six six six sound suspicious to me? Why does six—
[Speaker C] six
[Rabbi Michael Abraham] six say that this requires explanation, that something here can’t be random?
[Speaker C] Is that the difference between probability and plausibility?
[Rabbi Michael Abraham] It’s—
[Speaker C] The difference between probability and plausibility.
[Rabbi Michael Abraham] Okay, you can call it that too. Six six six is a special result. Special and rare are not the same thing. Every result of a thousand die rolls is rare—six to the minus thousand, that’s the probability of each of the results. Every result is rare, but not every result is special. After all, I know that a rare result will come out here. If you roll a thousand times, you’ll get a vector of a thousand results, a thousand places, one through six in a thousand places. Okay? So you know in advance that a rare result will come out. So the fact that a rare result came out shouldn’t surprise me. But when the result six six six six a thousand times comes out, that should surprise me. Why? Because the result—it’s not only because of the probability that it would come out, but because the result is a special result. Why did precisely this special result come out rather than one of the countless other rare results? And when I mark the result in advance as special and it happened, that really is something that requires explanation. But if the result that happened is rare without being special, that does not necessarily require explanation. So returning to my sister—since she lived in Jerusalem, Jerusalem is already a marked place; it’s special. If someone else comes here, if he’s from Jerusalem, that’s special. How did it happen that he came precisely from Jerusalem and not from a million other places? Here there really is room for wonder, for something that calls for explanation. In other words, it has to be special for me to be impressed by it. Now in the case of Bible skips, if you really choose, say, the number seven—suppose you decide that seven is a special number in the Bible and you have independently derived indications for that, and now you use seven specifically and you really find all sorts of results—that’s actually interesting. But if you find it with some other number, well, it was bound to come out with some number. So if I choose some number, I can always arrange it on the basis of some number and find any result you want. I’ll simply define the code accordingly if I’m free to choose the number as I please. Therefore if I marked the number seven in advance, that is much more meaningful than if I find it in 13,145. That too is interesting; the probability is the same probability, but it’s much less anomalous, much less in need of explanation. And the same thing if I can now arrange the code in a way that will bring me the special results—I’ve done nothing, right? In other words, if I find where Sadat’s murderer is written and find Sadat, and now I arrange a code whose result will give me exactly those two places—then true, if I had come in advance with this code and found Sadat next to his murderer, that would have been amazing, because I built the code with no relation to that, I didn’t know what it would give me, and it gave me exactly the correct information. That really is something that requires explanation. But if I find Sadat and his murderer in the same place and arrange a code that gives me that, that’s no trick. There are countless possible codes; I can always choose one of the codes that gives me the special result. Therefore, even though when you ask what is the probability that in this code Sadat and his murderer will be found next to one another—the answer is zero. But to the same extent, the probability is the same that it will be found in any one of countless other codes, and if I can choose any code I like, then in one of them it will come out, and I chose that one. That is exactly choosing; it is exactly an ad hoc lottery. Do you understand why it is exactly an ad hoc lottery? You are basically choosing the lottery mechanism so that it gives the result you want, like that person with the boat. He decided that genetics would be the lottery: whoever turned out physically stronger was the one whose lot it was to stay alive. Why did you choose the stronger one and not the weaker one? Or the letters of the name, or the date of birth, or I don’t know what, or the number of siblings? Because in one of the lotteries it will always turn out that you are the one who stays alive and all the others have to fall into the water. If you choose the lottery, the way the lottery is carried out, then that is not a lottery—you chose the result. That’s what I called an ad hoc lottery: you choose the code in the Bible and then it gives you fantastic results. That’s no great feat. You ran through all the codes and chose the code that would give you the fantastic result. That’s a very small achievement. That can be done in any book. If you give me the code in advance—or in other words you tell me, this code is unique from my standpoint, it’s not just some code I choose arbitrarily but a unique code—if you tell me in advance a unique code and it really gives you results, that’s impressive. But if you choose the code, then even though the probability is the same probability, a very small probability that the sequence of Sadat will come out next to Sadat—still, you understand, the probability in a given code is maybe one in a billion, but if I have a hundred million possible codes, then in a hundred such codes it may come out. If I choose one of them, then there is no problem. I can always arrange things so that I get this kind of information in any book I want; I’ll build the code accordingly so that it gives me all that information. And therefore—I’m not going into Bible codes again, I don’t have a very clear position on them beyond suspicions—but this claim is a serious claim and one that has to be checked seriously. In other words, how exactly did you formulate the code, how much do you play with it? Because that playing around is basically like choosing a code. If you choose certain parameters within the code, then in effect you are choosing one code out of many other codes, and you are choosing the code that will give you the result. That is not called a random result. If such a result comes out by chance, that’s surprising. But this is not a random result; you chose the code that would give you that result, even though given that code the probability that the result would come out is zero. But if you choose the code in order for it to give you the result, then I don’t care that the probability is zero, because the more correct question is: what is the probability that there will be some code that gives this result? Because if there is some code that gives this result, I’ll choose it. That’s the right question. And the answer to that question is one. There is always a code that will give you any result you want. I can build you a code that gives it. No problem at all. Tell me what you want to find in the Torah, next to what, exactly where, what you want to happen—I’ll build you a code that gives you that without any problem. It’s like the argument of Wittgenstein that I’ve brought more than once about following a rule. He shows there that it’s very easy to see that for any sequence of numbers you give me, and you ask what the next number will be, I can arrange the next number for you with no problem—I can arrange a formula that gives you all the first numbers and makes the next number whatever you want. And it makes no difference which one; there is always a formula that does it. That is exactly what I’m saying here. You are basically choosing the code so that it will give you the desired result, the result you wanted in advance. In other words, you chose the result. You have the result, and you choose the code that gives it. That’s not the same thing as saying: I chose a code, and now let’s see what results it gives me. That is the correct way to test. And if you choose the code in light of the result that you already know must be produced, you’ve done nothing. It’s drawing the target around the arrow. And that is exactly the problem with the ad hoc lottery we talked about on the ship to Liverpool. It’s an ad hoc lottery because you basically chose the mode of lottery that would give the result that you stay alive. Now true, it’s a free lottery and the probability that you would come out alive was equal to the probability of the other person. No problem. But there are lots of other such lotteries in which the probability is the opposite. You chose this lottery, and as a result you stayed alive. That is not called a fair lottery. You chose the result. And that is exactly the same as the claim against Bible codes. When you choose the mechanism so that it will give you a certain result, then the fact that the result has a small probability says nothing. You chose the mechanism so that you would get the result with the small probability. Like—I can choose the way the national lottery is conducted so that the ticket I’m holding will win. I’ll choose how to spin it; I know which ticket each spin produces, and I’ll choose the spin that brings out my ticket. After all, if you don’t know it in advance, then that spin is perfectly fine; some spin has to be made. And if I choose the spin knowing that the result it will give is my ticket, then you understand that this is not a fair lottery. Okay, that is exactly the problem of the ad hoc element. It seems to me this illustrates it well.
[Speaker B] Rabbi, one more question about that? Yes. If we suppose it wasn’t ad hoc—suppose those two who tossed the coin and the survivor didn’t know who was stronger between them, and he didn’t know in advance that he was stronger than the other one—then supposedly it could come out that maybe it’s fair. But I’m asking a different question. Suppose all the residents of a certain city decide that all conflict management… between them will be done by the method of whoever is stronger wins. Violence. Sodom. Then supposedly it’s fair—they accepted it. After all, the whole striving for fairness is against the rule of force. So here too, even if it wasn’t ad hoc, it contradicts basic fairness.
[Rabbi Michael Abraham] It’s fair not because it’s a fair lottery. It’s fair because everyone agreed. Suppose I agreed to give up—throw me into the water and you stay alive. That’s also fair, because I agreed. But not because it’s a fair lottery. It’s fair because I agreed, not because this mechanism is fair. I can agree to an unfair mechanism. If I agree, I can’t later claim that it’s unfair, because I agreed. But it still isn’t fair. Do you understand?
[Speaker B] And if in Sodom everyone agreed that they murder and that’s our method—after all, that’s what was there—then from that standpoint everything is okay?
[Rabbi Michael Abraham] If everyone agreed, everything is okay.
[Speaker B] That’s what was in Sodom—everyone agreed. Everyone agreed about the guests, not about themselves.
[Rabbi Michael Abraham] They agreed to do that to guests or to people who were not parties to that agreement. That’s not the same thing. The fact that everyone agrees about my fate when I come to stay there—that’s not what’s called fairness. If I would agree with them that when I come to you, you’ll chop off my legs because I have a large shoe size—fine, then I agreed. I have no complaints. You can no longer come with complaints.
[Speaker C] Rabbi, can I ask a question? Yes. A question from above the whole discussion. I mean, I want to argue that this whole discussion about lotteries, both in the case of the ship and in the case of Siamese twins, is unnecessary. Why? Because in fact the person who threw the others into the sea did not act according to a lottery. I mean, he didn’t make lottery-type calculations, like I’m stronger and they’re weaker. He just threw into the sea the first one who came to hand. And also in the case of Siamese twins, seemingly we don’t need to make a lottery. You can choose one of them and that’s it. That’s a lottery.
[Rabbi Michael Abraham] What difference does it make?
[Speaker C] No, that’s not a lottery.
[Rabbi Michael Abraham] Why not? What, a lottery has to be specifically with a coin? Any process of random selection is fine. Whoever I feel like throwing into the sea, whoever I feel like—I don’t know—separating from the Siamese twin, whoever I feel like sending to die, that’s also a kind of lottery, because I have no connection to them, so I choose one of them arbitrarily. That’s a lottery. It’s like a coin.
[Speaker C] But is that a fair lottery? Yes.
[Rabbi Michael Abraham] Okay. But the moment I’m the one throwing the other into the sea—not that some third party, I don’t know, decides between the two which one to throw into the sea, but I throw the other into the sea—that’s already problematic.
[Speaker C] Okay, okay, I understand.
[Rabbi Michael Abraham] Okay. Fine, so that’s just a supplement regarding ad hoc lotteries, and maybe also a bit about fallacies—we’ll get to that later. But now I want to continue what I started last time. And this is a question that came up in the course of things. Last time I distinguished between fate and a lottery. And I said that fate is according to God, whereas a lottery is random, and therefore fairness and all those things are needed. Now, Eli Merzbach’s claim in that interview he had with Jozefitz was that the randomness in the world is actually the way the Holy One, blessed be He, speaks to us, the way He runs the world. He says that a lottery is the Holy One’s way of hiding Himself and running what happens in the world covertly. And that was basically Eli Merzbach’s basic thesis in that conversation.
Now, if that really were the case—that is, if the Holy One, blessed be He, really runs everything that happens here in the world—then there is no difference between a lottery and fate. Obviously, right? A lottery and fate are the same thing. Even when I flip a coin to determine who gets which half of the land, or the whole land, when the land can’t be divided—if I flip a coin, then clearly, according to Eli Merzbach’s assumption, the Holy One, blessed be He, decided who would get that land. He caused the coin to fall on the side that would give me the land because He thinks I deserve it. That is his view; it’s the view of many, in my opinion most, most of those who think about this issue.
Now, if that were true, then it basically means there is no difference between fate and lottery. The whole distinction I made in the previous class is incorrect. Lottery and fate are the same thing; it’s all in God’s hands. Now if that is so, then the claim I made about fate I will now also make about lottery. If so, then there is really no importance to the question of fairness in the odds. Say I want to flip a coin between two brothers to see which of them gets the indivisible land, their inheritance. Do I need to make sure the coin is fair? Obviously not. So long as there is some principled possibility that the coin will fall on heads or tails. It doesn’t have to be fifty-fifty. Even if it’s ninety-ten or ninety-nine to one. It’s in His hands.
You remember we talked there about Moshe Koppel with the fixed case. We talked about… we have a hundred balls inside an urn: ninety-nine red and one black. Now I can choose whichever ball I want and look and take it out. What is the chance that I’ll take out a black ball? There’s one black ball and ninety-nine red ones.
[Speaker C] One percent.
[Rabbi Michael Abraham] Agreed? Fifty percent. The chance is fifty percent. Because if I like black, then I’ll go there, I’ll choose the black one and take it out. If I like red, then I don’t need to choose—I’ll just take out a red ball. It all depends on what I like. So what difference does it make how many balls are in the urn? In the end I’ll choose what I want. The chance that I want black or that I want red is fifty-fifty. If there’s no information, I mean. In the absence of information, I say the assumption is that if he likes red or likes black, it’s fifty-fifty. If he likes black, he’ll take out the one black ball there, because that’s what he wants. What difference does it make that there’s only one? Okay?
The Holy One, blessed be He—when He wants me to get the land, and let’s say the chance that the coin… the coin is unfair. The chance the coin falls heads is one percent. And heads will give me the land. And tails will give the other one the land. But if the Holy One, blessed be He, wants to give me the land, He will make sure the coin falls on the one percent. What’s the problem? After all, in the end He’s the one who makes what happens with the coin happen. He’ll make sure the coin falls on the one percent…
[Speaker B] Then every thief and every murderer will say: if God hadn’t wanted it, then I wouldn’t have succeeded in stealing and I wouldn’t have succeeded in murdering.
[Rabbi Michael Abraham] Right. Exactly. Meaning, there’s something here—this is of course an even graver claim—but it’s exactly the same thing. Very true, I fully agree. One has to understand that according to Eli Merzbach’s view, or the view… again I’m saying this is the accepted view, that basically everything that happens in the world that appears random to us is only hidden providence, yes, it’s… divine hiddenness. But really the Holy One, blessed be He, runs everything behind it, and to us it appears random. If that were so, there would be no importance whatsoever to preserving fairness in lotteries. No importance at all. In the end, the Holy One, blessed be He, does what He decides.
[Speaker C] Yes, yes, yes, but you’re assuming He has something to decide now. I didn’t understand. You’re assuming here that for the Holy One, blessed be He, this is relevant… that He cares to decide in this case. Maybe He… maybe He supervises everything.
[Rabbi Michael Abraham] That’s what they claim. If I get the land, apparently it was supposed to come to me.
[Speaker C] No, no, no—but in these cases there isn’t anyone who is the real winner.
[Rabbi Michael Abraham] Again, not because I am the owner of the land—it’s two heirs, there’s no true owner here—but because I deserve the land because I’m righteous. When they make a lottery, the Holy One, blessed be He, wants me to have the land because He wants to reward me for my righteousness. And my brother is less righteous, so he deserves the land less. So the Holy One, blessed be He, will arrange it so that I get the land. Their claim is that there is nothing random in the world. There is no chance in the world at all. Everything that happens in the world, even though it looks random to us, is really the hand of God. That is basically what he says. Therefore he said that the Holy One, blessed be He, basically runs the world or speaks to us through statistics or through randomness. So that is a view that basically says there is no real randomness in the world; it is all the work of the Holy One, blessed be He. So if that’s the case, then this whole idea of a fair lottery loses its meaning.
All right, so it’s not a huge attack. You could say: fine, true, then he’ll say indeed, correct, the coin doesn’t need to be fair. It just needs to be tossed, because that’s what the Holy One, blessed be He, wants.
[Speaker D] But it seems that God generally prefers to go with the majority; that’s also a problem. You hear? What—that God generally tends to go with the statistics, that’s also a problem in an unfair situation.
[Rabbi Michael Abraham] What—that God? I didn’t hear well.
[Speaker D] God tends to go with the statistics in general. So if we are in an unfair situation, then presumably most likely God will go with the majority. Why?
[Rabbi Michael Abraham] What do you mean, an unfair situation? I didn’t understand. Let’s say the coin is… the coin is ninety-nine percent in my favor, one percent in favor of my brother. Okay? Now we tossed the coin and my brother came out. Would anyone think there’s some kind of problem here? There’s no problem here, everything is fine.
[Speaker D] No, there’s no problem, but generally God likes to go with the higher probability.
[Rabbi Michael Abraham] And where do you get that from?
[Speaker D] I see when I look at reality and I say: generally, when I have a hundred balls and one black one and so on, generally what happens is that God goes with the majority.
[Rabbi Michael Abraham] What you see is not that God likes to go with the probabilities. What you see is that God is not involved and the probabilities determine the outcome. If they’re simply no longer relevant, then it doesn’t matter.
[Speaker D] That’s how it is—after all, an unfair lottery. I’m saying, it doesn’t matter what you call it.
[Rabbi Michael Abraham] Leave it—so what you’re really saying is that what I call God being involved is not correct; basically that… that’s what I call God’s involvement. Fine, if that’s what you mean, then indeed.
[Speaker D] I’m saying, even in their view, even if we take the thing that God—okay—then He’s also showing us that He wants to go with the majority.
[Rabbi Michael Abraham] If He wants to go with the majority, He goes with the statistics, then He’s not involved. Then the statistics are already doing what statistics do. Not involved. What do you need to say—
[Speaker D] You have to say—
[Rabbi Michael Abraham] involved, and then say yes but He doesn’t intervene because He goes with the probabilities. If He goes with the probabilities and He doesn’t intervene, then He’s not involved. You can’t tell me He’s involved but He always goes with the probabilities.
[Speaker B] I think that is what he’s claiming here, though.
[Rabbi Michael Abraham] Then that’s an absurd claim. If you always go with the probabilities, then you’re not involved. Then you let the probabilities decide.
[Speaker D] I’m coming to say that even in their view, seemingly they should see the word of God in the fact that He always goes with the majority. I mean, why should they stop the divine perspective there?
[Rabbi Michael Abraham] What does it mean that He goes with the majority? The majority does what it does, and the Holy One, blessed be He, comes afterward and says “blessed be He.”
[Speaker D] Right, that too can be seen in reality. They say let’s look at what happens, and from that conclude that apparently God wants this.
[Rabbi Michael Abraham] We see that many times God likes to go with the majority and with the probabilities. I’m not saying that the Holy One, blessed be He, doesn’t want the majority to win. On the contrary, He very much wants that. I’m saying He’s not involved. And they claim He is involved, not that He wants. That He wants—so what if He wants? I also want. I also think He wants. That’s not the argument. The argument is whether what happened here is the result of the hand of God, or whether what happened here is what every atheist non-Jew sees happening here. So if everything that an atheist non-Jew sees is also what you think, that’s what’s called God not being involved. Call it God involved, but everything happens by itself without His intervening. Well then that’s called not involved, so what is this word game?
[Speaker B] Those who argue that God is involved—then how can it be that He always obeys statistics? Completely, every time.
[Rabbi Michael Abraham] That’s what I’m saying. Therefore it’s pretty clear that He simply isn’t involved. That’s the reality. So the point is that according to the view—you can say, of course, according to Eli Merzbach’s view—you can say that indeed, yes, the lottery doesn’t have to be fair. Right? All these requirements for a fair lottery stem from a mistaken theological view. There’s no need for it. But this is already all over the halakhic decisors, the requirements that a lottery be fair. To the point that I think I brought last time that the Havot Yair says that even fate has to be fair, and not only a lottery. And here I argued that he is mistaken, because fate is not a lottery. But regarding a lottery, clearly it has to be fair, and everyone agrees. If the lottery is not fair, it says in all the decisors: if the lottery is unfair, the results are void. That was the discussion we had, Elihav, with the two people entered in the lottery with the same name—that it was supposedly an unfair lottery and therefore you argued the results were void—but no, that was a fair lottery. Fine, but let’s leave that.
The point is that at least if I adopt the view of the decisors—and it seems to me Eli Merzbach will not go against the view of the decisors; he comes to defend the accepted view—then I don’t understand how one can say what he says. It seems to me that it cannot be said.
Now I want to expand this a bit. Basically this question raises the question of the Holy One’s involvement in the world. Yes? Or, in our terms, doubt and statistics. I ask: what is statistics? If the Holy One, blessed be He, does everything in the world, then there is no statistics. Nothing here is random. Meaning, if I speak about statistics, at least in the accepted sense, that basically assumes implicitly that the Holy One, blessed be He, does not manage what is happening here. Not that He is not involved at all—that’s a more extreme statement—but that He does not manage what happens on an ongoing basis. Okay? That is the meaning of talking about statistics.
Now basically this is the same thing—or a parallel question to this issue—is the question of how one sees the hand of the Holy One, blessed be He, in the world. Is there hidden involvement, as it is called? The common claim today is that there are miracles today too, but they are hidden miracles. What does that mean? Something happens that in fact we have a natural explanation for, or we assume there is a natural explanation for even if we haven’t found it, but that still does not contradict the fact that this is the hand of God. Meaning, what happens by way of nature is also the hand of God.
Now here you have to pay careful attention, because this is very similar to what I said earlier about lottery. In this case it’s nature, it’s determinism; there it was randomness. But it’s really the same thing. The logic is the same logic. The claim in practice is that if indeed the laws of nature are correct—that is, if nature operates according to fixed laws—then that means there is no divine involvement. Because divine involvement—again, on an ongoing basis, I’m not talking about specific cases where one can argue, perhaps sporadically here and there He chooses to intervene and suspend the laws of nature—but in a place where things operate according to the laws of nature, which have not been suspended, there is no room to talk about the involvement of a divine hand. Because that is exactly like saying there is involvement of the Holy One, blessed be He, in statistics, except that He always wants the statistics to work—so He is not involved.
The Holy One, blessed be He, is supposedly involved, but gravity will always determine what happens, or electromagnetism, whatever, the laws of nature. So that means He is not involved. Maybe He wants what happens—presumably He wants what happens because after all He created those laws—but it happens because of the laws, not because of the Holy One’s involvement. He did not decide the result that occurred; rather, the laws of nature brought about that result. He only created the laws of nature.
Why do I say this? Because as far as we know, at least aside from very very tiny microscopy in quantum theory, in all other contexts and scientific fields our world is completely deterministic. And what does “completely deterministic” mean? It means that if you give me the state of reality at a given moment, I will tell you what will be at the next moment. Deterministic—it’s dictated, there are no different possibilities here; I will tell you what will happen at the next moment.
Now, if I claim that the Holy One, blessed be He, is involved, the meaning is that at the first given moment there was a state X; according to the laws of nature, Y should have happened, because the laws of nature are deterministic; but Z happened, because the Holy One, blessed be He, intervened. “Intervened” means He changed what should have happened according to the laws of nature without His intervention, right? If He intervened and caused Y, that’s not called intervening—Y would have happened even without His intervention. If He intervened, that means Y did not happen, what should have happened according to the laws of nature; He suspended the laws of nature, and instead Z happened.
So the involvement of the Holy One, blessed be He, is always a deviation from the laws of nature. There is no such thing as involvement within the framework of the laws of nature. There is no such thing. If the laws of nature allowed two different outcomes to occur from one given state, then there would be room to say that the Holy One, blessed be He, chooses which of the two outcomes will occur, and both are compatible with the laws of nature. Then there would be room to speak of divine involvement within nature. But if nature is deterministic, then there is no room for divine involvement within nature. Every divine involvement means a miracle. Maybe a miracle we won’t see with our eyes, we won’t notice there was a miracle, but there was a miracle there.
When I pray to the Holy One, blessed be He, and ask Him for healing, then if I was supposed to recover by the medical treatment I am undergoing even without the Holy One’s help, then I don’t need to turn to Him. I turn to Him because I fear a situation in which the medical technique will not help me, and I ask Him to help me instead. In other words, to intervene and alter the natural course of events, to suspend the laws of nature, to act differently, not according to the laws of nature. I cannot ask the Holy One, blessed be He, that the laws of nature should work. I can, but that’s just unnecessary chatter. The laws of nature work, don’t worry—you don’t need your prayers for that. The laws of nature work. If you pray to the Holy One, blessed be He, it is always a prayer asking Him to intervene and bring about an outcome that the laws of nature do not determine, a different outcome from what would have happened according to the laws of nature. Otherwise this is not divine involvement.
So therefore all this talk about divine involvement within nature is just confusion. You can say there is divine involvement in a miraculous way, in a way that I don’t notice there was a miracle—of course that’s possible, no problem. But you cannot say this is divine involvement when it happens in parallel to the natural course of things. It’s not. There was an unnatural course here, only maybe I didn’t notice, maybe I didn’t see, with every little thing that happens. But something has to happen there that is not according to the laws of nature. Otherwise there is no divine involvement. Talking about divine involvement within nature is simply conceptual confusion. By the way, this doesn’t belong to a worldview—it’s just a mistake. There are so many—
[Speaker D] How is this different from free choice? The claim you just raised can also be applied to free choice. If B is supposed to come out and everything is deterministic, then where is—
[Rabbi Michael Abraham] I absolutely say this also with respect to free choice. When a person chooses freely, he changes the natural course of things.
[Speaker D] Excellent, so it could also be that God enters into these changes.
[Rabbi Michael Abraham] I didn’t say He couldn’t. Only if He changes the laws of nature. What I’m claiming is that there cannot be involvement of the Holy One, blessed be He, within the framework of… the laws of nature. That is not possible. Or to suspend them—the One who forbade is the One who permitted. He created the laws of nature and He can also suspend them. But there has to be a miracle. Divine involvement is always with a miracle. There is no natural involvement, there is no such thing. That is an urban legend that is widespread in works of Jewish thought and among various Jewish thinkers and others, but it is simply total nonsense. There is no substance to it. It is conceptual confusion. One can talk about involvement in the tiny quantum domain, but even there it won’t help, because involvement in the tiny domain won’t change anything in the large domain. There is smearing at the larger scales. Quantum effects do not appear at the large scale. And if you make sure they do appear, then again you have intervened. And besides, even involvement in a quantum random event is involvement. When you determine the result of the lottery and don’t let the lottery run freely—that too is involvement. Involvement in the laws of quantum theory, in the statistical laws of quantum theory. There is no such thing as divine involvement that is within the laws of nature. It is simply an oxymoron, nonsense. It is not. Why not?
[Speaker C] Why not say that He intervenes by operating the laws of nature? That by operating the laws of nature, by bringing them about, He acts through them?
[Rabbi Michael Abraham] No, fine, I have no problem with that, but that is not what is meant when people speak about divine involvement. Obviously you can say that first of all He created the laws of nature. You can also say that the ongoing operation of the laws of nature is always nourished from Him. He somehow keeps it running on an ongoing basis. I have no problem with that. That’s perfectly fine. So long as you agree that the laws of nature are basically managing the matter—perhaps by the power of the Holy One, blessed be He, it doesn’t matter to me. But it is conducted according to the laws of nature. Okay?
Someone who talks about divine involvement basically says that everything depends—for example, if you performed commandments then the Tylenol will bring your fever down. If you didn’t perform commandments, it won’t bring your fever down. Because the Holy One, blessed be He, doesn’t want it to bring your fever down. No—if I take Tylenol, it will bring my fever down. Unless there is a miracle. The Holy One, blessed be He, will intervene and say whoa—suspend the Tylenol or what it did and leave my fever high. He can do that. Usually that doesn’t happen. I tend to think it doesn’t happen at all, but that is already a question I need to discuss separately. But within nature it cannot happen. Here this is beyond the realm of disputes—this is not arguable, it is simply nonsense. Okay?
Now understand that this is exactly the same logic as saying that the Holy One, blessed be He, hides behind lotteries. “The Holy One, blessed be He, hides behind lotteries” means that it is not a lottery. He gives the land to the one who deserves the land, not to the one for whom the coin fell favorably. He makes the coin fall so that it falls there. No lottery took place here; no lottery was conducted here. It is simply an act of the Holy One, blessed be He, which to our eyes looks like a lottery, but that’s just a mistake. Because we don’t see that really it is the Holy One, blessed be He. Same thing with the laws of nature, exactly as with lotteries. If you say lotteries are lotteries and the laws of nature are laws of nature, then take the Holy One, blessed be He, out of the picture. He doesn’t belong here.
[Speaker C] If He is here then—
[Rabbi Michael Abraham] then it’s not a lottery and it’s not the laws of nature.
[Speaker C] What is the meaning of the blessings that we go to receive from rabbis or wonder-workers and so on?
[Rabbi Michael Abraham] Whoever goes to receive blessings from rabbis, and even more so from wonder-workers, should on that very occasion also ask them what the meaning of this act is. I’d be happy to hear the answer.
[Speaker C] So a blessing means that we pray that the Holy One, blessed be He, will intervene for you and change your situation?
[Rabbi Michael Abraham] Not only a blessing—why go there? What about the Amidah prayer, where I ask Him to give me livelihood and healing? Do you need to go to wonder-workers for that?
[Speaker C] It’s more merit—meaning if it’s a blessing that comes from a rabbi or a wonder-worker, it has more power. What? I didn’t understand. It has more power because fundamentally there is—
[Rabbi Michael Abraham] That’s what you think, I don’t know; I don’t think so. But leave it—why go there, to a place that can be debated? There’s the Amidah prayer, leave the wonder-workers. Ali Baba and Bava Kamma. Go to the Amidah prayer. There you pray for healing, you pray for redemption, you pray for livelihood.
[Speaker C] So also for rain. Certainly, certainly—I pray that the Holy One, blessed be He, will intervene and change the—
[Rabbi Michael Abraham] Ask from there, don’t ask from the wonder-workers.
[Speaker C] I’m not asking, I’m claiming. I mean, I’m saying that prayer is that the Holy One, blessed be He, should intervene and change the existing situation.
[Rabbi Michael Abraham] Correct. So if you’re not asking, then everything is fine. I thought you were asking something.
[Speaker C] But is that the role of prayer according to your view as well?
[Rabbi Michael Abraham] Those parts of prayer—the requests. Obviously. And therefore I say: if I had the power, I would abolish it. But right now, again—if I were convinced that the Holy One, blessed be He, does not intervene at all, I would not say it. It would just be empty words, as the Talmud in Yoma does say about the fact that they abolished “the great, mighty, and awesome God,” that they abolished it because the Holy One, blessed be He, hates falsehood; His seal is truth. The fact that I am obligated to pray is very nice, but if I don’t think such a thing can happen, then it’s just lip movement. I wouldn’t pray for that.
I cannot be certain that He does not intervene here and there in a sporadic way, and therefore I do not have enough confidence to say that I abolish the… for myself; I am not the Sanhedrin. But I also do not stop saying it, because I cannot be absolutely convinced that there are no involvements here and there. And I am fairly convinced that there are no involvements on an ongoing basis. Livelihood, health, and everything else are generally not connected to the Holy One, blessed be He, in any way. And if there is some place where He does decide to intervene, maybe that can happen—then perhaps one can apply prayer to that. That if there is someone in need and there is no natural solution for his condition, then may the Holy One, blessed be He, help him. For that one can pray, in my view. For something concrete of mine, and certainly something for which I have a natural solution, I do not see what there is to pray for.
What yes? As Moses our teacher said there to Nahshon ben Aminadav—“Why do you cry out to Me? Speak to the children of Israel that they go forward.” No—the Holy One, blessed be He, says to Moses: “Why do you cry out to Me? Speak to the children of Israel that they go forward.” Why do you cry out to Me? Speak to the children of Israel that they go forward. If you have something to do, do it; don’t pray.
It reminds me of the story about Lithuanian stories, Hasidic stories, and Lithuanian stories. I like Lithuanian stories more. There was Rabbi Shlomo Kluger, the rabbi of Brody—that was a major Jewish city. Once two Jews came to him from some village near Brody to ask a question. They came to ask him a question. A difficult question; he couldn’t find an answer. The great Rabbi Shlomo Kluger couldn’t find an answer—embarrassing. He says: listen, I don’t know, I’m sorry. They went back home to their village and went to ask the village rabbi, some young fellow, not well known. They went to ask him; he went into the room and came back with an answer.
They return to Rabbi Shlomo Kluger and tell him: look, there is a young rabbi by us, a young fellow, and he gave us the answer to what you couldn’t solve. Incredible—a genius like that by you and I didn’t know? He summoned him to come to him in Brody. He said to him: tell me, how did you do it? How did you figure out the answer to that difficult question? He said to him: look, Your Honor, I’ll tell you the truth. They asked me that question, and I almost fainted. It was clear to me that I couldn’t answer it. I went into the room and prayed from the depths of my heart to the Holy One, blessed be He, to help me. Then my eyes happened to fall on some book that was sticking out a bit from the shelf. I took out the book, opened it—boom, right there in the spot was the answer to the question. Rabbi Shlomo Kluger threw him down all the stairs. He said to him: I thought you knew how to learn; all you know how to do is wail. You know how to cry. You need to know how to learn, not how to cry. Those are Lithuanian stories.
Anyway, for our purposes: when you have something to do on the practical plane, you are not supposed to pray, you are supposed to act. If you have nothing to do, and you ask that perhaps nevertheless the Holy One, blessed be He, will decide for some reason to intervene in this case and not let nature manage things—fine, pray, maybe it will help you; most likely not. But maybe yes, that can’t be ruled out.
Anyway, what I want to say is that behind this discussion about lotteries and fates there are really conceptions, or a much more fundamental and deeper discussion, touching on the involvement of the Holy One, blessed be He, in reality in general. And the question is whether, when I see reality operating through lotteries or through natural laws, I can still say that really this is being directed by the hand of the Holy One, blessed be He, or not. And the answer is no. Here this is a categorical answer. There is no room for discussion. Anyone who says otherwise is simply mistaken. Confused. He can say that there are places where God suspends nature and acts in its place—about that one can argue. He cannot say that God acts within nature; there is no such thing.
And therefore that is basically what lies behind the distinction I made between lotteries and fates. Because my claim is that in lotteries the Holy One, blessed be He, is not involved and is not supposed to be involved, because I am not doing this in order to receive an answer. There is no answer. I am doing it in order to distribute the chances equally. With fates I do it in order to receive an answer, and there I expect the Holy One, blessed be He, to be involved and to give me the answer. And therefore there truly is no issue there that the fate be fair. That is really not important.
All right, anyway, that is regarding the involvement of the Holy One, blessed be He, in the world. Now I come to the next chapter. In the next chapter the question is: so how do people nevertheless arrive at the conclusion that the Holy One, blessed be He, is involved? And about that I already spoke; it’s what I said before. This raises a more fundamental question. Clearly within nature the Holy One, blessed be He, is not involved. But it may be that there are situations in which He intervenes and suspends nature. Yes? He makes this situation an exception to the natural course and decides on a different outcome. That can happen. Once in a while, I don’t know, here and there it can happen. I can’t rule it out categorically.
But—and here is the next point I want to get to—the question is whether we have any way of knowing that this is happening. People who report miracles, things that happened to them that are improbable, illogical, unnatural, and therefore clearly the Holy One, blessed be He, helped, intervened, saved—things of that sort. So up to now I dealt with the question whether a priori this is possible. The answer is yes. A priori it is possible, although I am rather skeptical about whether it actually happens in practice; but I don’t know, I can’t rule it out. Here and there it can happen.
The question, however, is whether I can look at a situation and understand that it really did happen. In other words, is this a falsifiable theory? Can I look at a situation and say: okay, here was the hand of God, this cannot be chance, and therefore here there was probably that sporadic involvement I spoke about earlier. So let’s look a bit at a few examples.
[Speaker C] Wait, are you asking in a certain sense or not?
[Rabbi Michael Abraham] Even statistically. Yes, not with certainty. There is no certainty about anything, but statistically. So here we come to the issue of fallacies, what I call the law of small numbers. Not I call it that—Daniel Kahneman calls it the law of small numbers. The law of small numbers means that what happens with large numbers also happens with small numbers. Not a true law, of course. There is the law of large numbers: with large numbers things obey statistics. Small numbers do not obey statistics, or do not necessarily obey statistics. “The law of small numbers” is Daniel Kahneman’s name for a fallacy, a fallacy of people who look at small numbers and think that what happens with large numbers also happens with small numbers. And that is a mistake.
[Speaker C] No, I didn’t understand, I didn’t understand. What?
[Rabbi Michael Abraham] I didn’t—
[Speaker C] understand what large numbers and small numbers are.
[Rabbi Michael Abraham] I’ll now bring a few examples and illustrations; this is our next topic, because this is the topic of statistical fallacies. Fallacies in statistical thinking. Okay? So let’s see, for example, one simple case. Yes? Somebody tells a story: he had a Book of Psalms in his pocket. There are stories like this here and there; there are also stories about the New Testament, don’t worry, there’s everything. There was shelling or gunfire, something like that, and a bullet got stuck exactly in that Psalms book. He forgot to take it out of his pocket before he went into battle, and it stopped the bullet and he was saved. Therefore, clearly there was the hand of God here and He saved him.
You know they say there are no atheists in foxholes. When you’re in a foxhole under bombardment, everyone suddenly becomes a believer in the Holy One, blessed be He. People often see this as an indication that deep down inside all human beings there is faith somewhere. I actually see it as the opposite indication, because usually after those guys get out of the foxhole, nothing remains of their religiosity. They can vow great and mighty vows when they’re in the foxhole, and after the Holy One, blessed be He, saves them they say: okay, we managed, thanks. And they forget all the religiosity that struck them there in the foxholes.
So too with these stories about the Psalms book. What is the problem with such a story? Seemingly the chance is very, very small, and he happened to forget, and exactly this happened—it’s all true. The question that needs to be examined in order to assess this rationally is to ask ourselves: how many people had it happen that they had a Book of Psalms and the bullet hit the other pocket and they died? How many people did not have a Book of Psalms and were saved with some other book, or without a book, simply because they were saved? How many people did this happen to at all, relative to the chance that such a thing would happen? There is some chance that such a thing would happen by chance even without involvement of the Holy One, blessed be He. So if there were, I don’t know, a hundred people in that same bombardment with Books of Psalms in their pockets, and one of them was saved because of a Book of Psalms, that doesn’t mean some miracle happened to him; it means the one-in-a-hundred statistic happened to occur to him.
I’m trying to give an example here of a situation where, at first glance, the event looks like an event with a very, very low probability. But as we saw earlier, low probability does not necessarily mean that there was some outside involvement here, that there is something here demanding explanation. You have to examine the context; you have to do the relevant statistical calculation. Therefore, looking at specific situations is usually a misleading perspective.
And I want for a moment to move to a completely different plane, to a completely different field where these fallacies occur. From Gaza to Gush Katif, it seems to me—or to the Gaza envelope, but I think Gush Katif, this was before it was evacuated—and all these miraculous miracles there, and how people were saved, lo and behold. And all of that was, in my opinion, nonsense from beginning to end. Really, just a concentrated collection of foolishness for kindergarten children. Like most of those books, that’s how they are. Nobody really bothered to check what the real probability was that such a thing would happen. Nobody did statistics: how many places came under shelling of that kind, and how many were hit in the other places, as against the righteous people of Gush Katif who weren’t hit, or were hit but only a little.
You understand that this is not a serious argument. Now on the one hand, when you are in that situation, as I said earlier, there are no atheists in foxholes. When you are inside such a situation, you are sure that a miracle happened to you. It is natural to relate to things that way. But when you really try to examine, systematically and rationally, whether there really was a miracle here, whether there really is an indication of divine involvement in such a situation, then for that you really need to do a more serious investigation. You need to check what the chance is that this would happen, as against how often it did happen relative to how often it did not happen.
[Speaker C] In simple terms, say there is a one-in-a-million chance that the shot falls exactly on the book and so on. Then it is more reasonable to assume that the Holy One, blessed be He, intervened than to assume that exactly this one-in-a-million case happened. Not at all.
[Rabbi Michael Abraham] Because if there were another million people with a Book of Psalms and it didn’t hit the book, then in one out of the million it did hit. So what?
[Speaker C] Yes, but there weren’t a million people who had—
[Rabbi Michael Abraham] Who says there weren’t? Did you check throughout all of history? Not only in Gush Katif. You have to check throughout all of history. Gush Katif is one case, and it happened in one case; check a hundred other cases.
[Speaker C] So you need to check a million people who had a Book of Psalms and someone shot at them. Yes.
[Rabbi Michael Abraham] Or a million—why? Again. This is not about a Book of Psalms. I’m now talking about Gush Katif; that’s not a Book of Psalms. Gush Katif is missiles that were fired and somehow they hardly hit. People, or there was little damage, and so on. Who says it was little? Given the precision level of Gaza’s missiles, I don’t know, thirty years ago, twenty years ago, thirty years ago, I don’t know how long—not like today, when it’s somewhat better, not much better but somewhat better. At that level of precision, when you fire at small communities in an area of that type, do some kind of statistical calculation. I didn’t do it, I don’t have the data, I didn’t do comparisons to other places. I very much doubt you would find statistically significant results. I tend to think not. But again, I too didn’t do the calculation.
[Speaker E] Rabbi, a person who is looking for a miracle and sees a miracle in this thing—say he really wants to come and check it scientifically—I don’t understand what result he’s supposed to reach. Because if he really discovered that it was an exceptional case, then as the rabbi said before, that’s still according to statistics; it’s still not exceptional in that sense. So I didn’t understand what would have to happen, yes?
[Rabbi Michael Abraham] It’s rare, but not necessarily exceptional.
[Speaker F] The Israeli Artillery Corps has probability tables for hitting a target—soldiers standing, lying down, and so on. I have such a table, something from the seventies; at the time it was relevant regarding… The chance of being hit is very small. I was under shelling a lot, I was even wounded in one of them. Thousands of shells—you get hit. But I must confess today: when my grandson drowned in a swimming pool eleven years ago, the rabbi here sent a question asking how the child was. I said, what are the doctors in the emergency room saying, and the rabbi wrote on WhatsApp: “We’re praying.” And I said to myself—I confess my sin—if the rabbi is praying, surely the child will come out of it safe and sound. And indeed, that is what happened—fact.
[Rabbi Michael Abraham] The rabbi is me, don’t get confused. Fine, there’s—
[Speaker D] “I confess my sins”—whose sins is he mentioning now? Huh? Whose sins is he mentioning?
[Rabbi Michael Abraham] My sins. Anyway, the point is that—
[Speaker C] So what would be a result that should be obtained in order for us to say that there is divine intervention?
[Rabbi Michael Abraham] A very difficult question. Usually it will be very hard to become convinced of that.
[Speaker D] That’s exactly the challenge, like free choice. It’s exactly the same issue, with the same thing that it’s hard to prove. Certainly one can argue that it exists and that it’s common; we just don’t have statistical proof, but one can argue…
[Rabbi Michael Abraham] You can argue anything. It’s only if you bring me proof from a case—there is no proof. You can argue anything. By the way, you could also argue that I was saved… you can argue anything, but when people publish a book about the miracles of the Holy One, blessed be He, and bring proof from the low statistics, that’s a mistake. You can claim it because that’s what you think, fine, health and happiness. And usually when people bring these kinds of cases, they use the case as proof for what they already think, but there really is no proof.
[Speaker E] Rabbi, I’m trying to ask whether, say, suppose they actually did the work and did the statistics, and really the reasonable odds were that there should have been many more casualties and everything, but still, still the possibility that they wouldn’t be harmed still exists. Meaning, I don’t understand why that simply doesn’t just come down to probability.
[Rabbi Michael Abraham] Because in a place where the probability is very low and something happened, I’m willing to accept the claim that there was divine involvement. But you have to do some kind of analysis here to see whether the probability is really low. Because you can’t—like I say—you toss a coin and you get one, one, zero, one, zero, zero, zero, one, one, I don’t know, some sequence. The probability of that is zero, so the Holy One, blessed be He, probably produced that result? Or in the lottery, my ticket won the lottery, so that means the Holy One, blessed be He, probably helped me, right? Because after all, the chance that my ticket would win the lottery is negligible. But you understand that that’s not true, because in the lottery drawing there were another million tickets, and each of them also had a negligible chance, but one of them comes up.
[Speaker E] So that’s why it’s not special.
[Rabbi Michael Abraham] Yes, exactly. No—because it’s not special. If it were special, that would be something else. But because it’s not special, the fact that it’s rare doesn’t say very much.
[Speaker E] I hope I’m not getting ahead of something here, but suppose there’s always the rabbi’s story about the accident, so in that case it is special, but the rabbi does use it to illustrate that…
[Rabbi Michael Abraham] No, that case is not special. Because the fact that I was saved—the exact same thing could have happened to anybody else; there’s nothing special about me. It’s a rare case, but not an exceptional one. But I’ll get to the case of the accident; that’s next. I’m getting to it. Not right now, I can already see, but I’ll get to it. Okay, let’s stop here. Sorry for being late, but once again with the fast I wanted to have some kind of food break.
[Speaker C] You still haven’t eaten yet.
[Rabbi Michael Abraham] Any other comments or questions? You’re still in the fast, Eliav, right?
[Speaker C] Yes, another two hours.
[Rabbi Michael Abraham] Okay, so goodbye, have an easy fast. Thank you very much, have an easy fast. Thanks.