Doubt and Probability—in Halakha, Jewish Thought, and Beyond—Lesson 24 – Rabbi Michael Abraham

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[Rabbi Michael Abraham] For a count, meaning: the fact that this requires investigation means that something happened here that objectively calls for investigation, even though the definition of “specialness” is a subjective definition. Like that woman there at the lake: since she was from Jerusalem, then for her Jerusalem was a special place. Now suppose someone from Jerusalem showed up. If he had just come from Jerusalem and she hadn’t been there, or someone else had been there, nobody would have blinked. But if she is from Jerusalem, then in her eyes the outcome involving Jerusalem is special. Now someone from Jerusalem happened to arrive, so a special result occurred here. But why is it special? It’s special only because someone was there before, someone was there, also a resident of Jerusalem, the person who had been there before. That’s a subjective matter. If she hadn’t been there and someone from Jerusalem arrived, then it wouldn’t have been special. Why not? What’s the difference?

[Speaker C] So she should have asked: what is the probability that I, as a woman who came from Jerusalem, would randomly meet someone who also happens to be from Jerusalem? The question is really about me, basically.

[Rabbi Michael Abraham] No, but that’s exactly the point. Suppose now that I’m there and I’m from Jerusalem, and there I ask: what’s the probability that someone from Jerusalem will show up? Very small. But I could also ask: what’s the probability that someone from Tokyo will show up? Also very small. The same probability. The probability—even the conditional probability—is the same probability. Meaning: what is the probability that someone will come from Jerusalem given that I’m from Jerusalem? It’s the same probability as: what is the probability that someone will come from Tokyo given that I’m from Jerusalem? Even the conditional probability is the same probability, and still Jerusalem given Jerusalem arouses wonder, while Tokyo given Jerusalem does not arouse wonder. The specialness of Jerusalem is subjective, and the probability built on it is the same probability, and still there’s something surprising here, something that calls for thought. Maybe someone invited him, maybe someone told him there’s a Jerusalemite sitting there and it’s worth dropping by to see, maybe you know each other. There’s the alternative explanation, right? There’s some alternative explanation that says why someone from Jerusalem arrived: because they told him some woman from Jerusalem was sitting there and he thought maybe he knows her. Just as an example. So you can also propose this thesis of the alternative explanation here. But I’m showing you that even though the probability is the same probability, there is some surprise created as a result of the specialness of the outcome. And the specialness of the outcome is truly in the eye of the beholder, it’s subjective—but it has objective consequences. Once we defined specialness, from that point on the same probability will look strange, unlike something else with the same probability that won’t look strange. There’s something very tricky here, and hard to understand. Fine, that was just a remark I added. In any case, back to our subject.

So we spoke about conditional probability, and I want to show you through two examples an application of this idea, or a mistake that comes from this. Someone once at the institute at Bar-Ilan asked me about the Sefer HaChinukh, which says that in a religious court we follow the majority. So the Sefer HaChinukh says: because the majority has a higher chance of hitting the truth. So he asked: suppose a judge gets to the truth with probability p. We already did calculations like that. Suppose he gets to the truth with probability p. So the probability that the judge is right is p. So, given that Reuven murdered, what is the probability that the judge will determine that Reuven murdered? p. Okay. Now suppose there is another judge who independently examines the question and reaches a conclusion whether Reuven murdered or not. What is the probability that he too will conclude that Reuven murdered? p. Also p. Suppose the quality of the judges is the same, both are p, same quality. So what is the probability that two judges will say that Reuven murdered? Since it’s independent, p squared. p times p. The probability that this one says he murdered times the probability that that one says he murdered. Because I want both of them to say he murdered. So it comes out that the probability that two judges are right is smaller than the probability that one judge is right. So what is the Sefer HaChinukh saying? p squared is smaller than p. Right, because p is a fraction. So p squared is smaller than p. If p is 0.8, then p squared is 0.64. So the probability that two judges are right is 0.64, and the probability that one judge is right is 0.8. On the contrary—then we should follow the minority, not the majority. That’s what he asked. By the way, this was someone who specialized in statistics; the question seemed strange to me, but that’s what he asked.

Another question he asked me was about menstrual cycles. Yes, you know there is a law regarding a woman’s cycle: when there is concern that she may see blood, then she is forbidden to have relations with her husband; there are certain distancing rules that have to be observed. Okay. Now what is a cycle? It’s around a month, but it can be various intervals, and therefore if a woman has a fixed cycle—say she knows that she sees blood every twenty-seven days—then if twenty-seven days have passed since the previous cycle, even though she still hasn’t seen blood, she and her husband must keep their distance, because there is concern she may see blood; she has an established pattern of seeing blood every twenty-seven days. Okay. That’s when she has a fixed cycle. What happens when she doesn’t have a fixed cycle? Or how do we decide that a woman has a fixed cycle? If the woman saw blood three times at the same interval. If she saw blood three times at the same interval, that means she has a fixed cycle. And from then on I am concerned for that fixed cycle. If not, then there is an average cycle and other things. But I’m talking right now about a fixed cycle, a cycle based on an interval.

So what he asked me was this. He said: doctors know how to say that women’s cycles are around a month—say between twenty-seven days, twenty-eight days, and thirty-one days. Almost all women fall between twenty-eight and thirty-one. That was the claim; I don’t know, that’s what he said. Okay. So think about it: a woman saw blood at fixed intervals three times. By the way, this is really about two intervals, not three. She saw blood, then after twenty-seven days blood again, and after another twenty-seven days blood again. All right? She saw it three times. What is the probability that she has a fixed cycle? We assume she has a fixed cycle after she saw it three times. What is the probability that this is correct? Seemingly, let’s do a little calculation. Suppose she saw—let’s say we’re talking about three intervals, not two, all right? So the woman saw blood after twenty-seven days. What is the probability that, given that she does not have a fixed cycle, she will see blood in the next two times after twenty-seven days? Again after twenty-seven days, and again after twenty-seven days?

So like this: if I have twenty-eight—sorry—if I have four possible cycle lengths, twenty-eight, twenty-nine, thirty, thirty-one. Almost all women are, say, in these numbers, or twenty-eight through thirty-one. So there are four possible intervals, right? So the probability of each interval, assuming it is randomly distributed, is one quarter. Right? So if now she got an interval of twenty-eight, what is the probability that the next interval will also be twenty-eight? One quarter.

[Speaker G] Twenty-five percent.

[Rabbi Michael Abraham] One quarter. What is the probability that the interval after that will also be twenty-eight? Again one quarter. So the probability that the next two intervals will be twenty-eight is one sixteenth. Right? Given that the first one was twenty-eight. Of course the same calculation applies to twenty-nine, thirty, and thirty-one. So practically speaking, the probability of getting a sequence of three identical intervals is one sixteenth.

[Speaker B] Rabbi, I don’t think they can hear. What? There’s a problem with the Zoom audio.

[Rabbi Michael Abraham] Oh yeah? Nobody can hear?

[Speaker F] Now they can hear, now they can hear. It got disconnected before.

[Speaker B] Ah, before you were talking and we didn’t hear anything.

[Rabbi Michael Abraham] Ah, now they can hear? Now yes. Okay, so I’ll go back briefly. There are four possible intervals for almost all women, between twenty-eight and thirty-one days. Okay. Now let’s assume the first interval was something, twenty-eight. The probability that the next two intervals will also be twenty-eight is one sixteenth. Because each interval has four possibilities: twenty-eight, twenty-nine, thirty, and thirty-one, let’s say with equal probability. A woman who doesn’t have a fixed cycle gets intervals with equal probability. I’m just making a rough estimate. So if the first interval was twenty-eight, it’s just some value. It doesn’t matter at all what it was. I’m asking: what is the probability that the next interval will also be twenty-eight? One quarter. The probability that the one after that will also be twenty-eight is another quarter. So the probability that the next two intervals will be identical to that interval is one sixteenth, assuming independence. Right?

Now, a woman sees blood in our times, at least, over roughly forty years. Okay? That’s the average, as I understand it. Roughly forty years. How many sequences does she have over forty years? How many months are there in forty years? About five hundred, right? Four hundred eighty is twelve times forty, so about five hundred months. Okay? Now five hundred months means that if it’s around once a month, she saw blood about five hundred times during that period. More or less. Okay? Out of all the sequences that occurred there—you see, this echoes what I was talking about earlier—how many of those sequences will be consecutive sequences of three identical ones?

[Speaker G] I don’t have some formula for that.

[Rabbi Michael Abraham] Why not? Of course there is.

[Speaker G] Because if it’s one sixteenth like we said before, then over five hundred months, yes, it comes out about one in four, roughly. One in thirty. Okay, one in thirty, yes, mathematically.

[Rabbi Michael Abraham] Thirty times we’ll get a sequence of three consecutive identical intervals.

[Speaker G] If—

[Rabbi Michael Abraham] If there are five hundred months, then how many sequences of three are there in five hundred months? Five hundred.

[Speaker G] One two three, two—

[Rabbi Michael Abraham] Two three four, three four five, four five six. That’s four hundred ninety-eight sequences. Meaning roughly five hundred sequences. Right? Now out of these five hundred sequences, the probability is one sixteenth to get a sequence of three consecutive times with the same value. That same identity. Meaning: thirty times, a woman who has no fixed cycle at all, thirty times she will see three consecutive periods of the same interval even though she has no fixed cycle, it all happens randomly. So on what basis do you say that if she saw a fixed cycle three times, then that’s her cycle? And now from this point on you have to be concerned for a fixed cycle? That’s absurd. After all, thirty times in her life, even if she has no fixed cycle whatsoever and everything is random, she will still show a uniform triple. So why suddenly? How can you infer from that that after she saw it three times this is a fixed cycle? This already sounds like a better question than the one about the judges.

[Speaker G] A question about what the presumption of regularity is based on.

[Rabbi Michael Abraham] What do you mean?

[Speaker G] It could be that women’s systems changed a bit.

[Rabbi Michael Abraham] No, no, no. Let’s not change anything. We’re talking about today’s reality. And in today’s reality too, we establish a period for a woman. Meaning a fixed cycle for a woman.

[Speaker G] Or maybe the whole “three times” is a presumption in the words of the Sages, and that’s how they treated it.

[Rabbi Michael Abraham] But it’s not really a substantive presumption. True, that’s certainly possible. It connects to things we discussed earlier in the series. I talked about inferring from three occurrences. Right? We had lessons on a three-time presumption. So yes, it’s connected to that, and a three-time presumption in the simple sense. These three times—there’s no logic at all in inferring a conclusion from them, so you don’t create a three-time presumption. We saw the Mekor Chayim on the laws of leavened food. If you don’t have some explanation behind these three occurrences, you won’t generate a presumption. And here I’m telling you that even if the thing is completely random, sequences will emerge—lots of sequences of three times. This woman will see thirty sequences of three times. So the fact that such a sequence occurred—does that mean she has a fixed cycle? After all, even on the assumption that the cycle is completely random, it will happen to her thirty times in life, a sequence of uniform intervals. So why infer anything from such a triple?

[Speaker E] But why should it come out consecutive? What? Why would it come out consecutive, exactly?

[Rabbi Michael Abraham] Three consecutive times, not continuously forever. A triple.

[Speaker E] Yes, why would it come out three times in a row?

[Rabbi Michael Abraham] Because the probability is one sixteenth, that’s what comes out. Think about it. It’s basically like rolling a die with four possible outcomes. All right? Now you fill five hundred—you do five hundred rolls, and each time it can come out either one or two or three or four. Okay? Completely parallel to what we talked about before. Now you identify somewhere along five hundred rolls—you understand that along those five hundred rolls, on average, you will identify such uniform triples of two-two-two or four-four-four.

[Speaker E] Why is it one quarter? Usually the cycle moves between twenty-one days and thirty-five days.

[Rabbi Michael Abraham] I said between twenty-eight and thirty-one.

[Speaker E] But in reality it’s between twenty-one and thirty-five days.

[Rabbi Michael Abraham] I don’t know. That was the datum he gave me. The datum he gave me was between twenty-eight and thirty-one for most women in the world. Meaning the vast majority. There are those who are out in the Gaussian tail, but that doesn’t matter. Most women in the world are between twenty-eight and thirty-one, that was the claim. Now if that’s so, then the discussion is a statistical discussion; I’m not going to get into the laws of menstrual cycles now. For the sake of discussion, let us assume that this really is the reality. It moves between twenty-eight and thirty-one. And now they tell me: so basically you have four possible outcomes, and you make five hundred rolls of a four-sided die. Meaning, it can come out one or two or three or four, and I roll it five hundred times. You understand that out of those five hundred times I will find on average thirty uniform triples of two-two-two or one-one-one or four-four-four. Thirty times. I’ll also find quadruples, by the way, not only triples. Even quintuples, maybe. Yes, I will find them. A quintuple—that is, a quadruple—no, a quintuple has probability one in two hundred fifty-six. Sixteen squared. Sixteen squared is two hundred ninety-six, right?

[Speaker G] But we’re talking about four days, right? If we start broadening it, that also broadens things too, it—

[Rabbi Michael Abraham] Then it’s no longer five hundred numbers. Obviously. I’m talking about four days for the sake of discussion. Okay? So two hundred fifty-six, one in two hundred fifty-six, when you have five hundred numbers, then you’ll have one or two of those too. Even a quintuple, not just a triple. Sorry, a quintuple, not a triple. Meaning, you’ll find such sequences all the time. So there’s no logic at all in inferring any conclusion from this. That was the second question.

So I told him that in my opinion he’s not right. Look, I’ll start with the judge in the religious court, because that’s actually something we already did. The judge in the religious court—what are you telling me? That the probability that two judges are right is p squared. What is the probability that both are wrong? The same thing? No. One minus p squared? No—one minus p, all squared. Because the probability that a judge is wrong is one minus p, so the probability that two are wrong is one minus p times one minus p. Okay. Right? But think about it: one minus p, all squared, plus p squared does not add up to one. Either they are right or they are wrong—how can it not add up to one? There are no other possibilities. Something here is broken in the calculation, right? That’s just an indication. Meaning: if the probability that they’re right were p squared, then by the same token the probability that they’re wrong would be one minus p, all squared. Right? One minus two p plus p squared, if you expand the parentheses. Okay? They do not add up to one. So if they do not add up to one, then those cannot be the probabilities for being right or wrong, because those probabilities have to sum to one.

And the reason for this—I’m not going to go through that calculation again, because it’s one we already did. When you do a conditional probability calculation, I’m not asking the question that Nadav asked: given that he murdered, what is the probability that they will say he murdered. Even that isn’t the right calculation, because when you ask that question, then you have to say, let’s suppose that two judges out of three say that he murdered. Right? Now, given that he murdered, there are two possibilities: either the two are right—sorry, there are two possibilities—either the two are right and the one is wrong, meaning he really did murder; or the two are wrong and the one is right, meaning the truth is that he did not murder. All right? Now I say: two say he murdered and one says he did not murder. What is the probability that he murdered? When you do the conditional probability calculation, you get what we did in previous lessons, and it comes out greater than the probability that a single judge is right. The probability that two are right is greater than the probability that one is right. Since it’s not p squared versus p; that’s simply an incorrect calculation. You have to do a conditional probability calculation, and I have to ask myself: given that they ruled this way, what is the probability that he really murdered, and what is the probability that he did not murder? Those two really do sum to one, and when you do the calculation you’ll see that the probability he murdered is higher than the conditional probability that he did not murder, given that two said he murdered. This is a calculation we already did. I’m only saying that this question that speaks in terms of p squared is basically a question that treats this as though one should calculate an absolute probability, and that’s incorrect. One has to calculate a conditional probability. Yes, intuition says that obviously if it’s two against one, and the judges are good, then the probability that the two are right is higher than the probability that the one is right. This isn’t a real question, it’s a paradox. Yes, not really a question—we talked about paradoxes in the past.

[Speaker C] Yes, Rabbi, I didn’t understand: the probability that each individual judge is right—what did the Rabbi say it is? What? In the question, what was the probability for each judge?

[Rabbi Michael Abraham] Given that Reuven murdered, what is the probability that the judge will say that he really murdered? p.

[Speaker C] And what is p? What would you prefer it to be?

[Rabbi Michael Abraham] More than one-half, if the judge is good. More than one-half, obviously. The worst possible judge is one-half, because then it’s just random—either he murdered or he didn’t, you can’t learn anything from such a judge. A judge who says he didn’t murder when he did murder is an excellent judge: just take what he says and do the opposite. This is the well-known Sma in section 3, that the opinion of ordinary householders is the opposite of Torah opinion. The moment you take a bad judge, he’s a householder, not a judge. Right? So the opinion of ordinary householders is the opposite of Torah opinion. Meaning, if the judge says Reuven murdered, excellent—then I know Reuven did not murder. That’s the story—I think I told it—about Sheinfeld, that Haredi writer, the Haredi hagiographer, publicist, who came to the Brisker Rav, and the Brisker Rav asked him: tell me, how do you always manage to hit on Torah opinion? What you say, even though you’re not such a great Torah scholar, somehow always matches what the great sages of the generation say. You always manage to hit on Torah opinion—which means, I add in parentheses, that you’re always saying nonsense. But the Brisker Rav says: how do you always manage to hit on Torah opinion? So he tells him: what’s the problem? I go out into the street, take a poll, and write the opposite. The opinion of ordinary householders is the opposite of Torah opinion, right? So that is true for judges: ordinary householders are bad judges. But judges who are bad in the sense that the probability is one-half—don’t do the opposite there, because you still don’t know what to do. The probability is one-half. Judges who are bad in the sense that the probability is zero—those are excellent judges. Yes, you know that riddle about the road to heaven. A famous riddle. You’re walking on the road to heaven, and you come to a fork with two paths. On one path stands a guard, and on the other path stands a guard. You know that one of them is a liar and one tells the truth. How can you, with one question to one of them, know which path leads to heaven? It’s a known riddle; I assume some of you know it. The answer is: you ask the first one, what would the second one tell me if I asked him which path leads to heaven? And then you do the opposite of the answer. Meaning, if I asked the truth-teller, then the other would lie to me, and the truth-teller tells the truth, so he will tell me the lie. Then I do the opposite of what he tells me. And if I asked the liar, then the truth-teller would tell me the truth, but the liar lies about what the truth-teller would tell me, so again he tells me a lie. So in every case, the answer I get—whether I asked the truth-teller or the liar—is a false answer, but that’s excellent that it’s a false answer. Why? Because if I know the answer is false, then I know the truth. He gave me the full information. Correlation one and correlation minus one are the same thing. Yes, if everything he tells me is the opposite of the truth, that’s excellent—it’s equally informative. Let him tell me what he says, and then I’ll do the opposite. The hard question is: what happens if I have one guard standing over both paths, and now I can ask him one question and infer which path leads to heaven? What am I supposed to ask him?

[Speaker G] Provided that you know whether he’s a liar or truthful?

[Rabbi Michael Abraham] If I know he tells the truth, then I’ll ask him. If I know he’s a liar, what will I do? I’ll also ask him and do the opposite, right? But what if I don’t know whether he’s a liar or tells the truth?

[Speaker G] You’ve arrived at conditional probability.

[Rabbi Michael Abraham] Why conditional probability?

[Speaker G] Either-or.

[Rabbi Michael Abraham] No, that’s not conditional probability. Either-or is just two possibilities. Conditional probability is when I know something.

[Speaker C] Anyway, once again it all depends on our definition of a liar. We are assuming that a liar is someone—

[Rabbi Michael Abraham] A pathological liar, who always lies.

[Speaker C] No, but the question is whether “liar” means someone who says the opposite of reality, or someone who tries to keep you from knowing the truth.

[Rabbi Michael Abraham] No, no. A liar means the opposite of reality.

[Speaker C] So as long as a liar is someone stable who says things in a consistent way. Right, exactly.

[Rabbi Michael Abraham] Therefore I say that such a liar is just as informative as a truth-teller—if you know he’s that kind of liar. Whatever he answers, do the opposite.

[Speaker C] Now if there’s one person—but if I tell him, I say to him, you know, Rabbi Michael Abraham will diagnose your solution—

[Rabbi Michael Abraham] Then he’ll diagnose me pathologically. You can’t—it is possible to ask questions; I have a book by Raymond Smullyan where he plays with this riddle. He does crazy things there. How you manage to answer in all kinds of constellations—you can really go wild with it in a wonderful way. A book of riddles by Raymond Smullyan, actually a nice book. Not easy. In any case: if we have one person and we don’t know what he is, a liar or—yet he is consistent. Either a consistent liar or a consistent truth-teller; I just don’t know which of the two. With one question, can I extract the truth from him? Or rather, not the truth, but the information.

[Speaker F] Ask him what someone who always lies or someone who always tells the truth would say about this path. Ask him what would be said—

[Rabbi Michael Abraham] Ask him whether he is lying to you or not?

[Speaker F] That won’t help. No, but it won’t help if you ask him what someone who always lies or always tells the truth would say.

[Rabbi Michael Abraham] No. Because if you ask him what someone who always lies would say, you still don’t know whether he will lie to you in answering that question or tell the truth in answering it. You might ask him, perhaps: what would someone of the opposite character from yours say? Meaning, if you are a liar, what would a truth-teller tell me; and if you are a truth-teller, what would the liar tell me. That’s one possibility. A second possibility: I ask him, what would you tell me if I asked you which path leads to heaven? You understand, that’s a double question. What would he have told me? He would have lied to me. And now he lies about what he would have said. So the answer to that question is one I should follow literally, not do the opposite. I should obey what he tells me if I ask him that question. Right? Ask him: what would you tell me if I asked you which path leads to heaven? Yes, but here there are errors, many errors; he can lie there too.

[Speaker G] No, no, I’m saying—

[Rabbi Michael Abraham] I don’t care whether he lies or tells the truth. It doesn’t matter to me. I can always extract the truth from him. It’s a logical polygraph. I can get the truth out of anyone, whether he’s a liar or a truth-teller. But I’ll tell you: there is a more sophisticated polygraph. I won’t get into it here—it’s complicated logical calculation. I once saw it in an article by Yael Cohen from the Hebrew University. She asked what happens if there is one person who is not consistent. Sometimes he lies, sometimes he tells the truth—not like before, where either he always lies or always tells the truth and I just don’t know which, but he is consistent. I just don’t know whether he is consistently lying or consistently truthful. Now there’s someone inconsistent: he decides arbitrarily, sometimes he lies, sometimes he doesn’t. Even from such a person you can extract the truth. But it’s sophisticated.

[Speaker C] So why don’t the police do this?

[Rabbi Michael Abraham] That’s the question I once asked in a youth science program. I taught them this truth-table, and then I asked: wait, so why doesn’t the police use this? But that’s—it’s a riddle. I think maybe I even have a column on my site about it. I seem to remember, I think so. Anyway yes, there’s some column, there once was a column about it. No, but that’s just as an aside. The point is that this is like—I’m remembering, today I’m a bit associative—there’s a theorem in game theory called Zermelo’s theorem. Zermelo’s theorem says that there is a family of games, from the family of chess-like games. A family of games satisfying certain conditions, for which you can determine in advance a winning strategy. They have a winning strategy. Meaning, either black wins in chess, say, or white wins, or it’s a draw, but this can be determined in advance. So you might say: what is this theorem saying? It says nothing. Obviously either black wins, or white wins, or it’s a draw. No—the theorem, that much I can also say, you don’t need a mathematical theorem for that. The theorem says: there exists one winning strategy. I don’t know what it is, but it exists. And that strategy determines that white always wins, or there is a strategy such that black always wins, or there is a strategy to force a draw. One of these is true. I don’t know which, but I can prove that only one of them is true. It’s not that the result of the game is decided anew each time—sometimes white wins, sometimes black. If you use the pure, absolute, perfect strategy, then the result of the game will always be the same result. It doesn’t depend on the abilities of the players. It doesn’t depend on who is facing you. Now that really is a theorem; that’s no longer trivial.

[Speaker C] If they discover that method, then chess is finished?

[Rabbi Michael Abraham] Correct. It’s just that it’s so complicated to formulate that strategy, because the number of possibilities on a chessboard is enormous. Therefore you cannot formulate and spell out what the correct move is for every board position—which is what a strategy means. A strategy means: give me a board position and I’ll tell you what you have to do. That’s called a strategy in chess. So you need all the possible board positions and, for each one, which move should be made now. That’s called a strategy, a strategy in a game of chess. So it’s a bit tricky, but it shows the difference between the existence of a fixed winning strategy—white always wins, or black always wins, I just don’t know which of the two strategies is the true one—and a situation in which there is no fixed strategy. Sometimes white wins, sometimes black; you can’t determine it in advance. Even a perfect supercomputer couldn’t determine it in advance; even the Holy One, blessed be He, could not determine it in advance.

[Speaker C] I understand, but suppose those two sides know this formula. A supercomputer—both sides have a supercomputer and both will activate this formula—

[Rabbi Michael Abraham] White and black—then there will always be one correct result. I don’t know what it is, but there will be one result. And both are supposed to win. What? Both are supposed to win? No. If there is a strategy for white, then black has no strategy. If there is a strategy for black, then white has no strategy. White opens; there is asymmetry in the game.

[Speaker C] Only because of the opening?

[Rabbi Michael Abraham] Obviously. Obviously it is either that white has a strategy and black does not, or that black has a strategy and white does not. And therefore I don’t know which of the two possibilities is true, but that is just my ignorance. It’s in the person, not in the object, okay? One of those two possibilities is true; we’re just not smart enough to know which. We are smart enough to determine that there is one answer. That we can prove. They prove it by induction. So an Open University course on game theory is devoted mostly to proving that theorem, Zermelo’s theorem.

In any case, why did I bring that up? Because there is a difference—this is the difference—between saying sometimes black wins, sometimes white wins, you can’t know, which is a trivial statement, obviously, and Zermelo’s theorem, whose result is not trivial: there is one winning strategy, either for white or for black, I just don’t know which of the two answers is correct. But only one of them is correct. That is not the same as saying that in every chess game sometimes white wins and sometimes black wins. That’s trivial; obvious.

[Speaker G] What does that give you?

[Rabbi Michael Abraham] It gives you knowledge in mathematics.

[Speaker G] No, that’s not what I asked. I asked: in the case where I know I have three strategies, each of which is either black wins, white wins, or a draw—

[Rabbi Michael Abraham] Only one of the three exists.

[Speaker G] Only one of them, right. Now suppose I do know that, but it’s impossible to exploit it, right? So I don’t have an explicit formulation of the thing. So I have nothing to do with it. Meaning, that knowledge didn’t do anything for me except let me sit there.

[Rabbi Michael Abraham] That’s not true. For the one who wins, that knowledge causes him to win. What do you mean? That knowledge causes him to search.

[Speaker G] Not necessarily that he’ll find it.

[Rabbi Michael Abraham] The one who loses has nothing he can do against it. But the winner, once equipped with that strategy, will always win. That’s the meaning of a strategy: the other side has nothing to do, he will lose whether he wants to or not. I can force him to lose. But it helps me: if I know that strategy, I’ll win every game.

[Speaker G] But you said it’s impossible to formulate it.

[Rabbi Michael Abraham] Correct, we do not know that strategy. This is what in mathematics is called an existence theorem. An existence theorem means that a solution exists. Sometimes one proves an existence theorem by a constructive proof. A constructive proof means: I build the solution and in that way prove that it exists. In this case we do not have a constructive proof. We can prove that a solution exists; we don’t know how to build it or find it. It’s not constructive. But it is still a theorem in mathematics. A theorem that adds to my mathematical knowledge. By the way, there are games where I can find that strategy. Games simpler than chess. For example, think about tic-tac-toe, right? You know it? A three-by-three board, and you have to fill a row of three with X’s or O’s. That game is much simpler than chess; it has a winning strategy, and the first player wins. Right. Sorry, no, no—here there isn’t—no, no, not the second player either. It’s a draw. Each side can force a draw. Nobody can force a win against the will of the other. Each side can force a draw. That I can prove constructively. I can build the strategy: for every board position I can tell you where to mark the next X or O, and then I have built the strategy for you. There aren’t many possible board positions here, so I can actually formulate that strategy. So here I can even prove the theorem constructively. What’s nice about Zermelo’s theorem is that the proof is non-constructive, and therefore it applies to this whole family of games, including games where I cannot explicitly formulate the strategy. And what is nice here is that once there is a theorem, then in certain games I can search for the strategy and find it, because I know it exists. Meaning, the theorem tells me it exists, and if the game is simple enough, I can search for it and I’ll find it too.

All right, I’ve gone too far afield; this isn’t our topic at all. I brought it only to show that there is a difference between the statement that in chess sometimes white wins, sometimes black wins, sometimes there’s a draw—which is a trivial statement—and Zermelo’s theorem, which says either there is a strategy by which black forces a win, or there is a strategy by which white forces a win, or there is no such strategy and a draw can be forced.

[Speaker G] At one point Perelman tried to do this, and I think he gave it up.

[Rabbi Michael Abraham] Tried to do what? Find the strategy?

[Speaker G] Yes. When he did the Poincaré conjecture, they asked him about it, and I think he dropped it and said not to deal with it. That’s how I remember it.

[Rabbi Michael Abraham] I haven’t heard that, don’t know it. In any case, to return to the liars and the desire on the road to heaven—there too there is a difference between someone who sometimes lies and sometimes tells the truth, who is inconsistent, and saying: I know he is consistent, either he always lies or he always tells the truth; I just don’t know which of those two possibilities is correct. That is not the same as saying this fellow sometimes lies, sometimes tells the truth, does whatever he feels like. Here you can see clearly that there is a difference, right? It’s not the same thing. And it turns out that even in that sophisticated case there is a strategy to extract the answer from him, the information. A logical strategy. You can’t really do it in practice, but it’s a logical strategy. Fine, in any case.

[Speaker C] Rabbi, I still haven’t gotten the story with the judges. I’m maybe not understanding. Again, suppose a certain judge is right in 80% of cases. Then another judge comes and says he is guilty, and he too is right in 80% of cases. So I should go and multiply that and reduce the chance that both of them are right? I don’t really understand how we got to that calculation.

[Rabbi Michael Abraham] No, on the contrary, obviously. I said that this calculation is incorrect. The question was: if you require two judges to agree, does that lower the probability? Answer: no, that’s not right—you made the wrong calculation. Because you did a non-conditional calculation, you multiplied the probabilities, but no, these are conditional probabilities. At the end of page 45 there is the calculation for whoever wants it, but basically I also did it in previous lessons.

In any case, what about menstrual cycles? There too, the picture is very similar. There too, what you really need to do is a conditional probability. You’re really saying this: when I talk about menstrual cycles, what question did I ask? The question I asked was: out of all the triples across a woman’s life, how many of those triples will be uniform triples? 1-1-1 or 3-3-3. Okay? That’s the question in one direction. What is the probability of getting a uniform triple? Given that the woman has a fixed cycle, what is the probability of getting a uniform triple? 1. Right? You definitely get a uniform triple because she has a fixed cycle. Given that she does not have a fixed cycle, what is the conditional probability of getting a uniform triple? 1/16. Right? Good.

[Speaker G] Yes, we just said that.

[Rabbi Michael Abraham] Yes. So if there are 500 triples, then it’s about 30; we’ll get 30 uniform triples. Okay? But those are the conditional probabilities of: given that she has a fixed cycle, what is the probability of getting a uniform triple? Given that she does not have a fixed cycle, what is the probability of getting a uniform triple? We know the answer: this is 1/16 and that is 1. But the question we are asking is the reverse question. Given that there was a fixed triple, what is the probability that she has a fixed cycle? Do you understand? I’m asking the reverse conditional probability. These calculations ask: given that she does not have a uniform cycle, what is the probability of getting a uniform triple? The answer is 1/16. Given that she does have a fixed cycle, what is the probability of getting a uniform triple? One. You are certain to get a uniform triple, right? That’s in one direction: given the woman’s reality, what is the probability of getting this kind of triple or that kind of triple. But when we come to determine a fixed cycle, we ask the reverse question. Given that the woman saw blood three times at the same interval, what is the probability that she has a fixed cycle? You understand that this is the reverse conditional probability?

[Speaker G] It’s like a complex world and God, God and a complex world, yes. Given…

[Rabbi Michael Abraham] That reversal we made there regarding the proof for God—exactly the same thing here. And again, it's a mistake that mixes up the directions of the conditional. I'm not asking: given that she has a fixed cycle, or doesn't have a fixed cycle, what's the probability of getting three uniform occurrences? Rather: if there are three uniform occurrences, what's the probability that the cycle is not fixed? And that's a completely different answer. And as we already saw—I won't do the calculation here again—but we already saw that the answer to that question depends on the question: what's the probability that a woman has a fixed cycle? How many women in the world have a fixed cycle? Now it turns out that if there is—I think, wait, I have the figure—as a result of a calculation, look at column 145, where I did the calculation. Yes, the ratio between the conditional probabilities—the probability that she has a fixed cycle given that she saw three uniform occurrences, and the probability that she does not have a fixed cycle given that she saw three uniform occurrences—wait, I'll put this up here. The probability of a fixed cycle, I mark as p of 1, yes, I mark it as q. Now when we do the conditional probabilities, what interests us is: given the case that she saw three consecutive occurrences. Given that she saw three consecutive occurrences, what's the probability that she has a fixed cycle? That's the answer in terms of p. Given that she saw three fixed occurrences, what's the probability that she doesn't have a fixed cycle? That's the probability. The ratio between those two probabilities is this. And q is the probability, or how many women have a fixed cycle. That's the probability. Now you understand that if, say, q is very small—if q is very small, then below it says 1 minus q, which is a number close to one, right? And above, q is very small, so the result is small. But if q is close to one, the result is huge. Meaning: if there are many women who have a fixed cycle, then such a triple would be an excellent indication that the woman who saw such a triple really does have a fixed cycle. But if the number of women who have a fixed cycle is small, then it's not a good indication. Okay? Now if 3% of women have a fixed cycle, the probabilities are roughly equal. Pretty amazing, but that's what comes out. If 3% of all women in the world have a fixed cycle, under the assumption… because there are very few women with a fixed cycle. So if 3% of women in the world have a fixed cycle, and I saw it happen three times in a row, the probability that she has a fixed cycle and the probability that she doesn't have a fixed cycle are fifty-fifty—they're equal. If the probability is more than 3%, then three times with a fixed interval gives me a good indication that this woman really does have one. And when you do the conditional probability calculation, you discover that a fixed cycle is actually a very good indicator, assuming that more than 3% of women in the world really have a fixed cycle. If it's really a very, very small percentage of women, then this whole thing is worthless. Now I don't know what the statistics are today, but it's a very small percentage of women who have a fixed cycle. I don't know exactly how much, what the data are today, so that would have to be checked. If it's less than 3%, you can throw interval-based fixed cycles into the trash, yes, fixed intervals.

[Speaker G] And what does it mean that it's impossible to test? What? Impossible to test.

[Rabbi Michael Abraham] Why? It's very possible to test—what's the problem? How many women have a cycle at a fixed interval all the time.

[Speaker H] Perplexity claims it's around five percent, a little less; I still haven't had a chance to verify it. Perplexity claims that the percentage of women who have a fixed cycle over a period of time is a little less than five percent. I haven't had time to verify it yet, I'm in the middle of trying to verify it—

[Rabbi Michael Abraham] —from the sources.

[Speaker H] A little under five percent, it says.

[Rabbi Michael Abraham] Okay, so if it's above five percent—above three percent is fine.

[Speaker H] Okay,

[Speaker G] How can you know that at all?

[Rabbi Michael Abraham] What's the problem? Do statistics among women—check.

[Speaker G] There aren't such statistics. We live in the Jewish world; Jews have—we check cycles and so on. Non-Jews don't check anything. Nobody knows anything about their cycles.

[Rabbi Michael Abraham] Fine, but you can check. Again, I'm saying it can be checked.

[Speaker H] Not that there is a study—what's the problem?

[Rabbi Michael Abraham] Do one. Take a sample of women and do statistics on a representative sample—what's the problem? Like any parameter, you can test it with a representative sample. There's no problem testing it.

[Speaker E] Again, it's a matter of data, but it also depends very much on for how long. Meaning, it may be that it doesn't persist over an entire lifetime. No, not an entire lifetime. Right, it may not persist over an entire lifetime, but it may persist for a period.

[Rabbi Michael Abraham] Say, I don't know, two years, I don't know how much.

[Speaker E] Even if we assume it persists for half a year, that's already a reason to be concerned about it.

[Rabbi Michael Abraham] No, exactly. It's enough if it persists for four months, because you already need to be concerned after three times for the next time. Right. What's the probability that the next time will also fall there?

[Speaker E] Yes. Okay, so the measure is half a year, not necessarily two years; it's not for life. I mean, the question is what data was actually checked by GPT, just saying—it depends a lot.

[Rabbi Michael Abraham] Well, it can—

[Speaker F] —be checked, no problem.

[Rabbi Michael Abraham] I think that this five-percent figure may be talking about those who have it like that their whole life. But those who have four fixed months—that's much more. But on the other hand, you know, those who have four fixed months—that could also be a result of our statistics,

[Speaker G] Are you familiar with the Israeli study?

[Rabbi Michael Abraham] It would distort the survey you do.

[Speaker B] By the way, there is such a study—

[Speaker G] —in Israel, yes, where a bank CEO earns two hundred thousand shekels and the street sweeper earns three thousand shekels, right, so the average salary is sixteen and a half thousand shekels. But that's not really—come on, it has to come out under some assumption, otherwise it just doesn't work.

[Rabbi Michael Abraham] Well, let's say if you take a whole lifetime, then it gives you some sort of bound.

[Speaker G] Yes, it's not—there are—

[Speaker B] —things that are impossible to test.

[Rabbi Michael Abraham] The probability of fixed intervals—understand, the probability of fixed intervals starting from, say, ten fixed intervals is already zero, the random probability. Meaning, among women who do not have a fixed cycle, to find a woman who saw ten times at a fixed interval—there's no such thing, it won't happen. That's it. That's what I'm saying.

[Speaker G] That's about one over—

[Rabbi Michael Abraham] —sixteen to the fifth power. That's a tiny number. No chance within five hundred months. Okay? So you don't need to go far; it's enough to check over a year, two years. If someone had a fixed cycle for a year or two, that's not accidental.

[Speaker G] Yes, but you understand that the moment you stop checking, it could get disrupted. Never mind. Fine, this isn't exactly mathematics. In the formula yes, but not in real life.

[Rabbi Michael Abraham] Statistics, when you apply it to life, always has assumptions—that's obvious. In life there are assumptions, what can I say—we sigh.

[Speaker E] You also have to remember: a cycle is not claiming to establish a fixed state, only a fifty-percent state. Mathematics—mathematics is logic, it's not science. It's not like a majority-based cycle, because it's not from the Torah, it's only rabbinic. The reason it's rabbinic is because it's only fifty percent.

[Speaker G] You're talking about rabbinic; we're talking about this.

[Speaker E] Even less than fifty percent.

[Rabbi Michael Abraham] That's the question. Do the calculation and see whether it's really less than fifty percent.

[Speaker E] According to the Jewish law that cycles are rabbinic, that means it's—

[Rabbi Michael Abraham] Less than fifty percent, because fifty percent is already a majority. Maybe the Sages were mistaken. Maybe the Sages were mistaken. Do the calculation and see whether it's less than fifty percent. And it may be that what you can say is: okay, we need to change the Jewish law and determine that cycles are Torah-level. Fine, possible. All right, uncertain impurity in the public domain, uncertain impurity in the private domain—we could do a little pilpul here about prohibition to her husband versus impurity, because we're discussing prohibition to her husband, so then it really isn't uncertain impurity, it's uncertain prohibition, and regarding her own impurity it may indeed be uncertain impurity. Fine.

[Speaker E] But why are you so sure there are views that hold it's from the Torah?

[Rabbi Michael Abraham] I'm saying, why should I care whether there are views or not? If I reached a mathematical or empirical conclusion that the probability is eighty percent, then I determine that it's from the Torah—why should I care about the views?

[Speaker G] For everything there's someone who holds it's Torah-level, for everything, that doesn't interfere with anything.

[Rabbi Michael Abraham] Not for everything. There are things that aren't. Poultry with milk—nobody says that's Torah-level.

[Speaker G] And even so, today you'll find endless things.

[Rabbi Michael Abraham] I don't know. Apparently you have special search methods; I don't find them. Anyway, that's it for now. Any comments or questions?

[Speaker G] By the way, a question—I just got back from abroad, someone asked me about meat and fish. Okay. What danger does that pose?

[Rabbi Michael Abraham] Meat and fish and all the delicacies, as they say.

[Speaker G] Yes, yes. No, in principle, from a Torah standpoint, I really didn't know what to answer the person. I told him that Maimonides doesn't bring it, so he shouldn't pay attention to it—but in principle—

[Rabbi Michael Abraham] But Maimonides does bring it, so what? As far as I know—I don't know.

[Speaker G] Nobody knows. The question is what the danger is.

[Rabbi Michael Abraham] So what's the problem?

[Speaker G] But there is no danger. So eat it. Certainly there is no danger. So eat it. Yes, but the question is how to relate today to this thing in all Jewish communities.

[Rabbi Michael Abraham] How should one relate to it? Eat it. It's not a prohibition; it's a prohibition founded on a health assumption. Once it becomes clear that the health assumption is incorrect, there is no prohibition. There's a factual mistake here.

[Speaker G] So here this is a case where the Sages were mistaken. Right. It's just that we were talking about cycles, so it came to mind now.

[Rabbi Michael Abraham] There are plenty more examples, no shortage of examples.

[Speaker E] There's always the claim that maybe they knew something we don't know.

[Speaker G] No, that's totally absurd, claims—

[Rabbi Michael Abraham] There are always claims. The truth is one.

[Speaker G] Yes, all the things people claimed about garlic and onions and eggs and all those—

[Rabbi Michael Abraham] Various dangers—those really are dubious matters. There is a claim that these are spiritual dangers; I don't know. But it doesn't seem from the language of the Talmud, and in the halakhic decisors it doesn't look like they're talking about spiritual danger. Let's put it this way: I'd bet that if we did a study between those who left an onion overnight and those who didn't leave an onion overnight, we wouldn't discover clear health differences.

[Speaker G] Exactly the opposite. Today they say it's good to leave onion, good to leave garlic, that it absorbs more healthy particles, pheromones and things like that—that's what they say. Fine.

[Speaker C] Rabbi, Rabbi, since people are already asking about meat and milk and all that and all the delicacies, can I ask about something a bit different? On the issue of unintended action, the topic of something unintended, yes, and then there's inevitable consequence, right? It concedes. How can there be inevitable consequence—inevitable consequence basically exists in every case, right? After all, there really isn't such a thing as not—

[Rabbi Michael Abraham] It depends on the dispute between the Taz and Rabbi Akiva Eiger, and I have columns about it on my website. Look there; search my site for epistemic doubt, or pseudo-ontic, sorry, pseudo-ontic. I have a series on ontic doubt and epistemic doubt, and one or two of those columns—or one of them, I don't remember—deals with pseudo-ontic doubt. Search for it on the site. You'll see that it's a dispute between Rabbi Akiva Eiger and the Taz, and I explain the two approaches there.

[Speaker C] Is there somewhere that the Rabbi really addresses in depth the dispute between Rabbi Yehuda and Rabbi Shimon in the context of inevitable consequence? Just to understand the dispute, because I can't manage to understand Rabbi Shimon's position.

[Rabbi Michael Abraham] Rabbi Shimon's? Why?

[Speaker C] Because he says, I didn't intend it. What do you mean? You knew it might happen.

[Rabbi Michael Abraham] It's not an exemption claim—

[Speaker C] No, it's—

[Rabbi Michael Abraham] I sent you to the lectures I gave on unintended action, where Rabbi Shimon isn't claiming that you're exempt because you're coerced, because you didn't know. It's an essential exemption: you didn't do a prohibition.

[Speaker C] Right, but why? How can that be? If this were a moral matter, yes? If this were a moral matter, you say: I didn't think about the immoral result, I didn't think about it, I intended something moral and it came out immoral—we ask you, but did you know that it might happen? I knew; I can't say I didn't know. It's not that I was coerced. Right. So obviously we'd hold you liable. Rabbi Shimon says no, you're completely exempt—it is permitted even ab initio.

[Rabbi Michael Abraham] Correct, it's permitted. That's the difference—that's exactly the point. In morality, when they accuse me, they're judging whether I'm guilty. In Jewish law, the discussion isn't whether I'm guilty; the discussion is whether I did a prohibition at all. You're not completely free of guilt, but what I'm guilty of isn't a prohibition.

[Speaker C] But in the end the act itself was an act of prohibition. He plowed; he did, he did—he plowed.

[Rabbi Michael Abraham] No—

[Speaker C] Physically, the action itself is an action of plowing.

[Rabbi Michael Abraham] There is no prohibition against plowing. There is no prohibition against plowing; there is a prohibition against plowing intentionally.

[Speaker C] No, but that's really—Rabbi Shimon is inventing that. Again, the Torah says do not plow. Wait, wait, the Torah says do not plow, and you're saying that if you—

[Rabbi Michael Abraham] The Torah doesn't say do not plow. The Torah says, “Do not do any labor.”

[Speaker C] And the Torah says that this labor is planned labor. And planned labor means labor that you intend. Let's leave the Sabbath aside, let's leave the Sabbath aside. In other areas besides the Sabbath there isn't planned labor. In other issues, simply, other topics that deal with this. A person performed an act. If we treat it as a moral act, like something where you commit a transgression, you bring about a result, an act that is immoral—when you say I didn't intend it, that isn't accepted, because you're negligent. Whereas Rabbi Shimon says it doesn't matter: if you didn't think about it, you intended something else, it is permitted for you, permitted from the outset.

[Rabbi Michael Abraham] And that's not inevitable consequence—

[Speaker C] I mean not in inevitable consequence. Right, but you knew it might happen.

[Rabbi Michael Abraham] I knew it might happen—so what? What happened?

[Speaker C] But why is it that with every moral act we don't say, no problem, it might happen, it might not have happened, everything's fine?

[Rabbi Michael Abraham] Right, because that's the nature of a moral act. What's that got to do with this?

[Speaker C] And why wouldn't a commandment be a moral act? Rabbi Kook, who thinks the entire Torah is a moral act—how would he understand Rabbi Shimon?

[Rabbi Michael Abraham] I don't know, ask him. I don't think that way.

[Speaker C] Right, so it comes out that the dispute is very interesting—Rabbi Shimon's position. It's not just incidental; it has to do with what the essence of commandments is. If it's something mystical, a repair, then it has to exist in the world.

[Rabbi Michael Abraham] I argue that Rabbi Yehuda also agrees with that. For Rabbi Shimon it's necessary; for Rabbi Yehuda it's possible, but that's not their dispute.

[Speaker C] So what is their dispute?

[Rabbi Michael Abraham] A different dispute: how I understand the Jewish law. Is intention part of the definition of the prohibited act or not? Or is the prohibited act an objective definition, and intention is some side parameter?

[Speaker C] It comes out that Rabbi Yehuda is very superficial, because it's as if he doesn't care what you think, only the result matters.

[Rabbi Michael Abraham] Superficial? He goes by the definition of the objective act. And Rabbi Shimon takes things into account. In fact some later authorities explain that they follow their general approach. That's why Rabbi Shimon interprets the rationale of the verse and Rabbi Yehuda does not interpret the rationale of the verse, because Rabbi Shimon goes after the reasons behind things and not after the thing itself. And Rabbi Yehuda focuses on the thing itself; he's an empiricist. Okay? Or the same thing in the Talmud in tractate Shabbat.

[Speaker C] But the Rabbi understands the implication here. I'm not really asking now about the dispute between Rabbi Yehuda and Rabbi Shimon; after all, it relates to our own day. When we discuss the question whether there's genocide in Gaza or not, the big excuse is that nobody decided on it. No—it's obvious to us, it seems reasonable, that neither Netanyahu nor Katz nor Gallant nor any IDF General Staff or Southern Command team sat down and wrote and decided, let's commit genocide. But it was convenient for everyone, and somehow they went along with it and said, we're constantly doing things, we're destroying all of Gaza, killing twenty thousand there—not because we're killing twenty thousand, because that's not genocide. Let's see what happens, and in the end, surprisingly enough, something happened that suited us very well.

[Rabbi Michael Abraham] And then we say we didn't intend it.

[Speaker C] And Rabbi Shimon says you're exempt.

[Rabbi Michael Abraham] Right, we're returning to an old argument. The claim is not unintended action. This is not an exemption claim of unintended action. It's not because, look, I didn't know, so I'm not guilty. I knew civilians would be killed.

[Speaker C] No, but it's not genocide because the UN convention says there has to be prior intent for genocide.

[Rabbi Michael Abraham] It doesn't require prior intent—no, no. It's not genocide because we were permitted to kill the civilians, not because we didn't intend it.

[Speaker C] Fine, that's not—I'm not talking about that claim, okay, that's a different claim. But many argue in the spaces—you read the discussions about it—a lot of Israelis, even those who argued against it, also when they spoke with me, said: nobody decided on it. No person decided on it. No document was found showing that someone decided to kill them as genocide, as a people.

[Rabbi Michael Abraham] Who are you—

[Speaker C] —talking to? Ask them, what do you want from me? I'm telling you—no, because I'm not addressing the Rabbi with the question whether it's genocide or not. I'm talking about the implication of unintended action in relation to that claim.

[Rabbi Michael Abraham] That implication isn't relevant according to my view. If there are people who use incorrect arguments to justify it, then find problems in their arguments.

[Speaker C] I'm talking within their view, I didn't come now to argue—

[Rabbi Michael Abraham] Rabbi—again—about this issue. According to their view, they're just mistaken. What's there to discuss in their view?

[Speaker C] Ah, so the Rabbi accepts that this argument is not—

[Rabbi Michael Abraham] It's not relevant at all in the moral aspect. What do you mean relevant? If you knew that someone would die, and you did what you did, and what you did was unjustified, but you knew that someone might die—not certainly—

[Speaker C] We're not talking about the number killed, we're talking about genocide, about a plan of genocide—

[Rabbi Michael Abraham] As if to carry out ethnic cleansing—

[Speaker C] —and then push them toward destruction as well.

[Rabbi Michael Abraham] There is no difference between genocide and any other crime. No difference whatsoever. When there is a moral crime, if you knew that this thing might happen, not with certainty, then you're negligent and you should be punished for it.

[Speaker C] It doesn't matter whether— But Rabbi Shimon says that if it's a Torah prohibition—

[Rabbi Michael Abraham] But commandments require intention—why don't you ask there? I do the commandment, but if I didn't say “for the sake of unification” beforehand, then I don't have a commandment. Why?

[Speaker C] No, because the moral act—if you do a moral act and by chance money fell from you and a poor person took it—

[Rabbi Michael Abraham] I don't understand. So why in commandments does that seem fine to you, but in transgressions not? Why?

[Speaker C] No, but the question is whether you knew about it. If you knew?

[Rabbi Michael Abraham] Of course I knew. I knew everything.

[Speaker C] What? Many times we read in the Jerusalem Talmud about amoraim who tell how they pray while they're thinking, counting sheep, and contemplating other things.

[Rabbi Michael Abraham] That's something else, that's something else. Someone performed a commandment without intention; he didn't say “for the sake of unification.”

[Speaker C] The question is what counts as without intention. Again, it's very easy to say that phrase, but it's not simple to understand what intentionless means. He got up in the morning. He blew the shofar for music. So here his whole intention, all his dedication, is for that, not for this.

[Rabbi Michael Abraham] Exactly. But he knows it's Rosh Hashanah today, and he knows you have to blow the shofar, but he doesn't want to blow it for the commandment; he blew it for music.

[Speaker C] The moral act that you're doing—clearly in such a case, where all your sacrifice was for your own sake, then it has no moral force at all. You can reduce it—it has no moral significance.

[Rabbi Michael Abraham] Move for a moment to other places. There's an asymmetry here. In commandments you receive something, and in transgressions you don't receive that same thing itself.

[Speaker C] Right, there is an asymmetry. Intention is significant.

[Rabbi Michael Abraham] In Jewish law, intention is very relevant.

[Speaker C] The inversion between transgression and commandment here isn't necessarily—it doesn't necessarily have to go together.

[Rabbi Michael Abraham] It's enough for me that it's not necessary; it's enough for me that it's similar in order to knock down the objection. To answer with difficulty is okay; to object with difficulty is not okay.

[Speaker C] But doesn't the Rabbi have some column just on the dispute itself between Rabbi Shimon and Rabbi Yehuda?

[Rabbi Michael Abraham] I have lectures on it. The lectures appear on the site, and the introduction to the lecture is exactly this: that it's not an exemption claim due to lack of guilt, but a claim due to lack of transgression. There is no transgression here. It's not that we pity you because you weren't guilty. It's not a claim of coercion. Therefore, therefore, the Talmud in tractate Pesachim says that where it was unavoidable and he didn't intend it, it's also exempt. What does “unavoidable and he didn't intend it” mean? So the medieval authorities (Rishonim) there explain. Say there are two paths to some place I want to go, okay? On one path there is an idol-worship perfume shop, and on the other there isn't. Now it's forbidden to smell the perfume of idol worship. But the path with the idol-worship perfume is fifty meters shorter than the other path. So the Talmud says: if I went by that path, I'm exempt. Now I knew I was going to smell the perfume of idol worship, and I could have gone by the other path—I'd have walked another fifty meters. I am exempt. Unavoidable and he didn't intend it.

[Speaker C] Even according to Rabbi Yehuda?

[Rabbi Michael Abraham] What? The Talmud links it to the dispute between Rabbi Shimon and Rabbi Yehuda, and the Jewish law rules, of course, like Rabbi Shimon. It's not at all clear why it depends on the dispute; that's a different issue.

[Speaker G] But Rabbi, that's not exemption—that's permitted even ab initio, that's something else.

[Rabbi Michael Abraham] Yes, correct—permitted. So why is it really permitted? If it were a claim of coercion—what kind of coercion is that? I won't walk another fifty meters? Walk another fifty meters. What coercion?

[Speaker G] Not related; it's not a claim of coercion.

[Rabbi Michael Abraham] There is—

[Speaker G] —no transgression here.

[Rabbi Michael Abraham] If I didn't do it this way, there is no transgression here.

[Speaker C] But not according to Rabbi Yehuda? According to Rabbi Yehuda there is. How does the Rabbi understand, for example, that aggadah? Still, the Rabbi doesn't like aggadot much, but it's really exactly connected. “How pleasant are the deeds of this nation”—what is that position of Rabbi Yehuda?

[Rabbi Michael Abraham] It's the same thing.

[Speaker C] What is Rabbi Yehuda saying there? “How pleasant are the deeds of this nation.”

[Rabbi Michael Abraham] That's what I came to say and then stopped. That's the Talmud in tractate Shabbat 31 that I started to mention, where Rabbi Yehuda and Rabbi Shimon also follow their general approaches.

[Speaker C] Right, but there—how do you understand Rabbi Yehuda? How can one understand Rabbi Yehuda?

[Rabbi Michael Abraham] Rabbi Yehuda continues to be detached from intentions.

[Speaker C] No, but that can't be. So what is he, a journalist? He sits there and says, you know, there are nice results here that the Romans built—they built bridges, they built… They are evil people, they wanted to do evil, they are corrupt to the core, they just destroyed His House and burned His Sanctuary, and they built interesting bridges—what are you, a journalist? You travel around the world, you're a journalist?

[Rabbi Michael Abraham] Show them gratitude for the bridges, and at the same time hate them with all your being.

[Speaker C] Why show gratitude for something they didn't even intend?

[Rabbi Michael Abraham] For the destruction of the Temple, you hate them.

[Speaker C] The explanation really doesn't give Rabbi Yehuda much kindness, because he comes out very strange. It's like saying about the Nazis: look, they built the stadium in Nuremberg, what a beautiful stadium.

[Rabbi Michael Abraham] Benefit where the other party doesn't lose. If I benefited, there is an obligation to pay for the benefit, even though I took it from you without your giving it to me, and even if you didn't lose anything. Then I have to pay you for the benefit. Benefit where the other party doesn't lose—why? The answer is because I benefited. I have to pay you for the value of the benefit I received from you. The same thing Rabbi Yehuda says: I benefited from the Romans because they built markets, bathhouses, things like that. True, they didn't do it for my sake, but I owe them something for the fact that they did it. Look at it like payment for benefit.

[Speaker G] We have this in our own times too. In every synagogue abroad, they pray for the welfare of the government and the state, even though they hate—and there are countries where this is the case—and that was also true in the time of the medieval authorities (Rishonim).

[Rabbi Michael Abraham] Certainly. You can, if they really also look after the Jews.

[Speaker G] No, they don't look after them. They don't look after them.

[Rabbi Michael Abraham] No, things are complicated, it's not that simple. There are also countries that persecute Jews, so maybe they persecute Jews, but there are also certain respects in which Jews benefit from there being a government.

[Speaker G] Fine, it's the same thing. Good, so that's the same answer. Right, and that was also in the period of the medieval authorities (Rishonim), also with Maharam who sat in prison and so on, and there too the community prayed. Okay. All right, friends—

[Rabbi Michael Abraham] That's all for now. Sabbath שלום.

[Speaker G] A blessed and peaceful Sabbath.

[Speaker E] Thank you.