Uncertainty and Statistics – Lecture 19

[Rabbi Michael Abraham] Last time we finished, we finished the conceptual discussion of the law of fixed status, and in the end I proposed one explanation that says that, in the end, my explanation was that a majority that is present before us is really a majority based on ignorance and not on positive information, whereas a majority that is not present before us is a majority based on information, like in science. And with a majority based on ignorance, it is really not generally correct to use statistics, because we do not have a distribution, and therefore we need the verse “follow the majority” to teach us that nevertheless we can go according to the majority, as in the case of ten stores. But that verse teaches us this only in a place where the piece separated from its place. And why? I explained, following Rabbi Shimon Shkop, that the moment the piece separates, I have ten sides: each store casts a side onto the piece — one side that it is kosher, another side that it is kosher, another side that it is kosher, and one side that it is not kosher — so there are nine sides that it is kosher. Each of the stores is basically a side regarding the piece, and we follow the majority of sides. In contrast, when the piece did not separate, then we are really talking about a piece whose doubt arose while it was still in the store itself, and so the discussion is really about the store and not the piece. The store did not separate from anywhere. Regarding the store, my question is whether it is kosher or not kosher, and here there are two sides, and therefore I should treat it as an even split. I explained even more than that, that the fact that the store belongs to the majority or belongs to the minority is a result of the statistical consideration, not the assumption. In the case of a piece that separated, I say: I have nine kosher stores and one non-kosher store, and since I have a majority of kosher stores, I infer from that that the piece too is kosher, because it probably separated from the majority group. But if I am talking about a piece that remains in its place, meaning inside the store, then true, there are still nine kosher stores and one non-kosher one, but my doubt regarding this store is not the question whether it belongs to the majority group or the minority group. My doubt about this store is whether it is kosher or not kosher. After I reach the conclusion that it is kosher, the result will be that it belongs to the majority group — but not that because it belongs to the majority group therefore it is kosher. Why in the world? It is not some more basic datum that it belongs to the majority group than the datum that it is kosher. On the contrary: if I reach the conclusion that it is kosher, then it turns out that it belongs to the majority group. Therefore there is no meaning here in using the concepts of majority, and so basically the stores are not casting sides onto this store. The only sides that exist here are two: either it is kosher or it is not kosher, and therefore this is like an even split. That was basically the claim, and I said—

[Speaker B] But—Rabbi, but on the real level, when a person is standing inside the store, he asks himself which store this is, because that will determine the kosher status of the piece. So he asks himself: if the stores here, most of them, are of this kind, then apparently this is such a store. This is just wordplay.

[Rabbi Michael Abraham] No, it’s not wordplay. Why is it wordplay?

[Speaker B] Again — the real question before a person when he’s inside the store is whether the piece is kosher and what this store is. Is the store I’m standing in part of the majority of stores that are kosher or not? So there is majority and minority, and statistically it’s obviously the same thing. So if Rabbi Shimon Shkop phrases it differently, does that change reality?

[Rabbi Michael Abraham] The doubt is what this store is. The doubt is not whether it belongs to the majority or the minority, because that’s not relevant, whether it belongs to the majority or the minority. The fact that it belongs to the majority or minority is not a datum from which I begin. On the contrary, after I reach the conclusion that it is kosher, I will reach the conclusion that it belongs to the majority. In contrast, with a piece that separated, then yes — because it most likely separated from the majority of stores, I reach the conclusion that it is kosher, and not because it is kosher that I infer it came from the majority of stores. So the doubt is genuinely structured differently here.

[Speaker B] If this were poison, like in the examples the Rabbi gave before, then wouldn’t the consideration be that if I’m in ninety out of a hundred stores, all of which are—

[Rabbi Michael Abraham] That’s what I was talking about. I would make that consideration out of ignorance. I would still bet on nine against one, even though that bet is made out of ignorance. But you can’t claim that this is a statistical consideration. It isn’t. And the question is whether I’m allowed to rely on a priori considerations that come from ignorance. The verse says yes. But without that, I shouldn’t have been able to rely on it in Jewish law. And therefore, since the verse says yes, we need to ask what the verse is talking about. It talks only about situations in which different sides are cast onto the thing I am judging, and we follow the majority of sides, because we learn it from a religious court. And we saw that in a religious court that is also the situation. So with the stores too, that’s how it works. But if the piece is inside the store, then there are no sides here, and that is not what the verse “follow the majority” was talking about. And the question is: if I were drinking based on that, I would indeed follow the majority. That’s true, but not as a statistical consideration. I’ve repeated this distinction many times. I make that consideration and eventually come to a conclusion — it’s like the coin or die when I have no idea whether they are fair or not, I would still bet that the chance is one in six, because if I have no information, all faces have equal weight. And that is not really because I know something, but out of ignorance. Same thing here. Except that a consideration out of ignorance needs a Torah source saying that one may rely on it in Jewish law. And that source is “follow the majority”, and it speaks only about a case of separation and not a case of fixed status. That was the explanation I proposed. There was also the explanation — I said last lecture — there was the explanation of Oren Reglit, and he argued that basically, let’s say I approach a store: I don’t choose a store randomly. I have my reasons. I like a kosher store, I like a non-kosher store, but I’m not just choosing a store for no reason. And because of that, you can’t use statistics here, because I’m not choosing the store randomly. It’s not a matter of random distribution. But if a piece separated from the store, the separation is a natural process. Nobody chose it, and therefore there I should use statistics. That was his suggestion. And we also spoke about the murderer who threw a stone into a group, and there too the question is whether he wanted to kill a Jew or wanted to kill a non-Jew. There really are two sides here — the question is what he wanted. The fact that there were nine Jews in the room and only one non-Jew — does that mean he wanted to kill a Jew? What does that have to do with it? It’s about what he wanted. And therefore in such questions it isn’t correct to use statistics. This somewhat reminds me of a distinction I’ve already made more than once with the majority concerning plowing. If I decide I want to buy an ox for slaughter, even though most people buy an ox for plowing, that’s my decision. I can decide to buy an ox for slaughter; there’s nothing unreasonable about that. You can’t tell me that what I’m saying is illogical because the statistics are against me. This is not a random process. I decide what kind of ox I want; I’m not holding a lottery about whether to buy an ox for slaughter or for plowing. It’s very similar to that distinction. The difference between these two explanations is that for Oren the basis of the distinction is that we’re dealing with an act of a choosing agent. When a human being chooses, then it isn’t a random process. After that I brought another example, of a mouse with pieces of leaven as opposed to pieces of matzah, and I said that Oren’s explanation can work there too, even though the mouse does not have choice in the metaphysical sense — it presumably doesn’t have free will — but it is still an act that is not random. Either the mouse likes leaven or the mouse likes matzah. And what it likes is not distributed according to how many piles there are in the warehouse. If there are nine kosher piles, matzah, and one pile of leaven, and the mouse took a piece, and now I ask whether that piece is leaven or not, the answer is fifty-fifty. Because if the mouse likes leaven, then it will go to the one pile of leaven out of ten. It’s deterministic — it’ll go straight there, because that’s what it likes. If it likes matzah, then it’ll go to one of the other nine piles. Its choice of pile is not random. It’s not drawing lots among piles. It goes to the pile it wants, like, if you remember, Kopel’s example of taking balls out of a jar. So I expanded Kopel’s example and asked: say there are ninety-nine red balls and one black ball, and now they tell me: choose a ball. And now I ask you, what is the chance that I choose a black ball? There is only one out of a hundred. And the answer is fifty percent. Why? Because I’m not reaching in and randomly drawing a ball. If I want a black ball, I will choose — there is no hole in this barrel — until I get to the black ball and I’ll take it. And if I want a red ball, then I’ll take a red ball. So the fact that there are more red balls than black balls increases the chance that I’ll take red only in a random process — only in a random process is that true. But in a process of choice that stems from some reason I have or from what I choose — a directed process — then there is no point in using statistics here. So that was the direction Oren proposed, and I said it is an interesting direction and there is a lot of logic to it. It doesn’t fit all the cases, but no explanation fits all the cases, and therefore I said that in any event the law of fixed status probably began with some basic cases for which there was also some logic. And after they established this rule that there is a difference between separation and fixed status, now we already use it even in situations where the original logic is not preserved, because Jewish law works with certain rules, and we are not now reopening every case from scratch. We do not require a judge to be an expert in statistics or a philosopher, and therefore it does not bother me if the application does not constantly preserve the original logic that was here. Okay, that was the first part. After that, at the end of last lecture, I moved into the question of majority on the time axis. We spoke about a woman who had relations and she is betrothed — yes, she is betrothed and she had relations. And now the question is whether she had relations after the betrothal or before the betrothal. Yes, the husband found an open entrance when he had relations with her for the first time, and the question is whether the woman had relations before the betrothal, in which case there is no problem and she is permitted to him because she was unmarried, or whether she had relations after the betrothal, in which case she is forbidden to the husband and to the man involved, and therefore forbidden to her husband as well. So the Talmud says yes, I have a doubt; it’s a doubt. So people asked me — they asked me on the site — why don’t we follow the majority on the time axis? Since for most of the time this woman was unmarried. One year she was betrothed — from betrothal to marriage is usually a year — so that was one year. So there are, I don’t know, from age three until age twenty or however old she was, let’s say seventeen years she was unmarried and one year she was betrothed. So if I don’t know when she had relations, why not assume that she had relations during the longer interval of time — those seventeen years — rather than during the single year? That was the question. I said that at first glance, the answer to that is very similar to the answer Oren suggested regarding the law of fixed status. Why? Because basically we are dealing here with a process that is not random. It is not a process distributed randomly, where the man and woman randomly choose a moment in time and have relations at that moment. That’s not how it works. They decide, based on various considerations, when to have relations, and of course it comes out at some moment in time, but they are not drawing lots among moments in time. That’s not the point. They have their considerations about when they want to do it. I said there is even a reason to do it before the betrothal — why not do it when she is unmarried? Fine, we said that’s probably not correct. But still, since there are considerations here and it is not a random process where we draw a moment in time, it is not correct to use statistical tools here. So that could certainly have answered the question of why I don’t follow the majority on the time axis here. But I brought another example there: what happens with a mikveh? Okay? A mikveh is a situation where, say, on Sunday I know the mikveh was full — forty se’ah, a valid mikveh. On Wednesday an impure person immersed in it; he wants to become pure, so he immersed on Wednesday. On Thursday suddenly I discover that the mikveh is lacking. So in such a situation, in principle, it is a doubt, except the question is whether we follow its original presumption or its current presumption, but in principle it is defined as a situation of doubt. And the question that arises here is the same question: why is this defined as a situation of doubt? Basically, this mikveh lost volume somewhere between Sunday and Thursday. From Sunday until then is four days. From Sunday to Wednesday, three days passed. From Wednesday to Thursday, one day. So if I need to decide whether the mikveh became lacking before Wednesday or after Wednesday, most likely it became lacking before Wednesday. So why don’t we follow the majority on the time axis in this case, but instead define this situation as a situation of doubt? Now here there is no difference anymore; here you can no longer explain it the way Oren would. Or the way I explained earlier only in Oren’s direction. Because here the choice of the moment in time when the mikveh became lacking is not a choice made for some reason, or a choice of a person, or even a mouse, or anything like that. It is a random process: at some point the mikveh became lacking. If so, this really is a lottery on the time axis. Why shouldn’t we follow the majority here? Here you can no longer resolve it in the way I proposed before. So that is more or less where we ended last time. What I want to propose is basically that there is an explanation here connected to the discussion I made earlier about the law of fixed status. Yes, in practice I am speaking about the question — say when I speak about the mikveh question, okay, then I am really speaking about the question of how we chose: at which moment on the time axis was the choice made? Which moment on the time axis was chosen? And since the choice is random, at least in the context of the mikveh, unlike the case of the open entrance, then since the choice is random, apparently I should follow the majority. And now I ask: ultimately we are dealing here with a majority that is present before us. There are, say, four days — Monday, Tuesday, Wednesday, or Thursday. Fine — Sunday, Monday, Tuesday, Wednesday, or Thursday — and I ask myself: which moment was chosen by the natural processes for the loss of volume of the mikveh? In other words, when did the mikveh become lacking? So I am basically drawing a moment from among the moments in time, and the question is why we should not assign that moment to the majority of moments, namely the interval before the immersion and not after the immersion. And the answer I want to suggest is that this is a case of fixed status. Because basically — think of it metaphorically, yes? — before me lies a collection of moments on the time axis. They are there, laid out on the time axis. It’s not space, it’s time. But if you look at it mathematically, it’s an x-axis, only the axis describes not space but time, no matter. But the time axis is basically laid out in some sense, the moments are on it, and I need to pick up, to take out, one of the moments. So I am effectively drawing a moment from among the moments of the time axis at which the mikveh became lacking. Now, once I draw a moment that is on the time axis, there has been no process of separation. It’s not that some moment left the time axis and now I ask where it came out from. Did it come out from the period between Sunday and Wednesday or from the period between Wednesday and Thursday? The question isn’t where it came out from; it is still there. It didn’t go anywhere. Therefore the question is: which moment is this? Is it the moment before or the moment after? If I decide that this moment was before, then the conclusion will be that it belongs to the majority of moments. But not that because it belongs to the majority of moments therefore it is before. Therefore, in this sense, that question is the same question I ask in the case of fixed status with a piece that is in the store. And here, since this is a majority that is present before us, I cannot follow the majority because the verse “follow the majority”, which is what tells me to go after the majority in a majority that is present before us, does not speak about fixed status. Since this case is one of fixed status, we therefore do not follow the majority here, and it is considered a doubt. That is my claim, and if that really is the explanation, then it works both for the mikveh and for the open entrance. Because the moment is always on the time axis, and in an essential sense, on the time axis the moment is always fixed. There is no separation of a moment on the time axis. And therefore yes, certainly these are the same kinds of questions in space as well. Yes, if I ask myself whether some item was closer to here or closer to there, I can also make spatial divisions, and there too I would say the same thing: those divisions are not relevant, because we have here the law of fixed status. Okay? Although again, here I must — and this is the important point — if I adopt the explanation that this is a matter of fixed status, then I am specifically forced to resort to my explanation of the law of fixed status, and not Oren’s explanation. Because Oren’s explanation depends on the question of how the moment was chosen: was there some factor that chose it for some reason, or was it chosen randomly? In this case it was chosen randomly, it’s a natural process. Therefore Oren’s explanation of the law of fixed status will not help for this situation. The explanation I am proposing will help for this situation. And again, I say, that does not necessarily mean Oren’s explanation is incorrect, because I said that none of the explanations really fits all the cases. We extend the rule that distinguishes between fixed status and separation after it has already been established. Now we already use it as it is, without constantly returning to the underlying logic on which it was based. Therefore Oren could tell me: okay, this doesn’t fit my explanation, but my explanation created the distinction between fixed status and separation, and once that distinction already exists, now I work with fixed status, period, without constantly revisiting the question.

[Speaker C] In the mikveh case, on Thursday it was discovered that the water was lacking, right? Yes. How can I know at all — I mean, your question is when it became lacking, but really why are you assuming it became lacking? Why not say it was like that the whole time? Where do you get the idea that it suddenly became lacking?

[Rabbi Michael Abraham] Because on Sunday I saw that it was full.

[Speaker C] On Sunday it really was full? Yes. Okay, so why not just benefit from the doubt? I only discovered it on Thursday. That’s the situation. On Thursday I discovered it, so then it became lacking.

[Rabbi Michael Abraham] But we are working with the assumption that doubts were not given simply so that one may enjoy them. What does “benefit from the doubt” even mean? We have laws of doubt. That’s how we operate. Why benefit from the doubt? If I have doubtful pork, doubtful kosher meat, should I just eat it and enjoy the doubt? There’s no such thing. The laws of doubt say that in a case of doubt we go stringently.

[Speaker C] Yes, but again, the first point in time at which you know it was lacking — that’s the only evidence you have in front of your eyes. Okay, and you have one more piece of evidence saying that it was full.

[Rabbi Michael Abraham] Sunday. On Sunday. Now somewhere in the middle the mikveh became lacking. The question is when.

[Speaker C] And this couldn’t have been discovered during those four days?

[Rabbi Michael Abraham] No. Again, if there are other indications — if it would have been discovered, and so on — then fine, you can weigh them, and of course they would enter the calculation. I’m talking right now about a case where no, it couldn’t have been discovered, it wasn’t discovered, and I have one datum for Sunday and one datum for Thursday. That’s it. That’s what I’m working with. That’s it.

[Speaker B] But why isn’t it obvious that it’s fifty percent? Even logically — if this weren’t a halakhic issue but, say, a medical one — you’d say: I don’t know when it became lacking, that entire span is doubtful, and throughout that whole span it’s fifty percent yes or fifty percent no.

[Rabbi Michael Abraham] What? Not at all. Not at all. Outside the halakhic context, obviously I would say it became lacking earlier. Most of the time, after all, was before the person immersed. Why assume that — why not assume that it became lacking during most of the… Think, for example, let’s make it extreme, okay?

[Speaker B] But it didn’t become blocked at that moment. It became blocked at the moment he immersed.

[Rabbi Michael Abraham] Fine, but I spoke about that in the previous lecture. For the sake of the discussion, I’m assuming it became lacking at a moment. I discussed that in the previous lecture. Now take an extreme case. Let’s say we had ten thousand days, not four. Okay? The person immersed one day before the end. Now ten thousand days earlier the mikveh was valid, and now the mikveh is lacking. Even then would you say fifty-fifty?

[Speaker B] Yes, I don’t know when it became lacking.

[Rabbi Michael Abraham] Of course you don’t know. I also don’t know whether a die landed on one or not one — does that make it fifty-fifty?

[Speaker B] The mikveh had exactly forty se’ah, but I don’t know when it became lacking, so I don’t know when. And if I knew that I immersed in the Kinneret and it was full—

[Rabbi Michael Abraham] You’re repeating the same point, so that explains nothing. The fact that you don’t know means I have uncertainty, and now I need to use statistics, right? That’s the role of statistics: to help me when I don’t know. Right? So now I don’t know. Why don’t you use statistics?

[Speaker B] But how does statistics help? I don’t know when it became lacking, so the whole time span is entirely doubtful to me.

[Rabbi Michael Abraham] Exactly — that’s what it means that you don’t know. If you knew, you wouldn’t need statistics.

[Speaker B] But the question is about the whole time span — as though the legal decision that follows from it, if I ask the question about every single point, is not necessarily correct.

[Rabbi Michael Abraham] If the person — the question is only about one time, not the whole time span. The question is whether the person who immersed one day before the end is impure or pure. That’s the question. That’s it. My question is whether at that moment the mikveh was valid, full, or lacking. That’s the question. And statistically, anyone will tell you it was obviously lacking.

[Speaker B] Why? Why? Why? On the first day it was valid. On the fifth day it was invalid. In the middle it changed, we don’t — so all the intermediate time, the interval, is unknown, and it’s fifty percent.

[Rabbi Michael Abraham] No. On the first day it was full. On day ten thousand it was lacking. One day before day ten thousand, a person immersed. Now ask a normal, sensible person on the street: what’s the chance—

[Speaker B] It depends whether from the outset we’re talking about the Sea of Galilee overflowing its banks, or a very limited mikveh. Not the Sea of Galilee — forty se’ah. Right, so exactly — with forty se’ah, since it’s limited, I have no idea when, the whole time is doubtful between them, from beginning to end.

[Rabbi Michael Abraham] Correct, the whole time is doubtful between them, and therefore we follow the majority.

[Speaker B] Excellent, we follow the majority. So why follow the majority here — no, fifty percent yes, fifty percent no, I have no idea. I have no reason at all to decide that it happened specifically on the first day, or the second, or third, or fourth.

[Rabbi Michael Abraham] Right — now our whole story starts again from the beginning. This whole series is about the fact that even when I don’t know something and there are two possibilities, that does not always mean fifty-fifty. You keep returning to the fact that I don’t know and there are two possibilities. I agree — I don’t know and there are two possibilities. Does it follow from that that the conclusion is fifty-fifty? Of course not.

[Speaker B] When I have a majority consideration, a statistical majority, then I follow the majority. But here, why is the statistical consideration correct? I don’t know when the mikveh became lacking. It could just as well have become lacking on the first day, the second, or the third, and that could have happened. Do you know which store the piece of meat came from — the one you found in the street? No. Is that also fifty-fifty? No, no — again, now we’re returning to the question of fixed status. I’m talking about the mikveh example. No, fixed status and separation.

[Rabbi Michael Abraham] You found a piece of meat in the street. Fine? There are ten stores, nine kosher and one non-kosher. Do you say fifty-fifty?

[Speaker B] No, I say it separated from one of the stores. Most of the stores — a thousand stores are kosher and one is non-kosher. We don’t know.

[Rabbi Michael Abraham] Kosher or not kosher — fifty-fifty. That’s what you told me here too.

[Speaker B] No, but it came — but here there is a certain logic: it came from some store. Here there are ten thousand seconds! No, but there is no logical reason to say that the majority means it became lacking at the last moment and not on the first day. The majority doesn’t say that.

[Rabbi Michael Abraham] Why doesn’t it say that? It became lacking — there’s no preference for one day over another.

[Speaker B] Right, it could be that it became deficient to exactly the same extent on the first day, and every day is fifty percent, every second is fifty percent yes and fifty percent no; out of those five days it’s fifty percent yes and fifty percent no, and on the fifth day it was certainly invalid.

[Rabbi Michael Abraham] No, no, not every second is fifty percent. Every second it could happen. And since every second it could happen, then presumably in most seconds it did happen.

[Speaker B] Suppose people immersed. Now the question wasn’t about one person, but about thousands of people who immersed every second. At every moment in time they immersed. So what would I say? Fifty percent immersed in a kosher mikveh and fifty percent did not.

[Rabbi Michael Abraham] Then you’d be mistaken if you said that. Why? Because the answer should be that all the people who are closer to the moment when the mikveh was full will be pure, and the people who are farther from the moment when the mikveh was full will be impure. That’s all. What do I care that a million people immersed? So what? My doubt about each one of them is a doubt about that person. That’s it. That seems simple to me. The only point is that there is a rule of fixed status here, that’s all.

[Speaker B] The fact that the time is closer doesn’t make it more kosher—that’s what I mean to say. It doesn’t make it more kosher.

[Rabbi Michael Abraham] I’m asking at what moment the mikveh became deficient.

[Speaker B] So by the same token—

[Rabbi Michael Abraham] Was there a particular moment at which it became deficient? Let’s assume that all the moments have equal standing. Then the probability for each of the moments that specifically in it the mikveh became deficient is equal. Since I have ten thousand days, the probability for each—

[Speaker B] such day is—

[Rabbi Michael Abraham] one in ten thousand.

[Speaker B] Right? I answered him by mistake, I wanted to silence it. Yossi, should I wake you up in the morning?

[Rabbi Michael Abraham] Wait, wait. Yossi, before the eyes of all Israel. Good. So I have the same probability for each of the days on which the mikveh became deficient. So the probability for each such day is one in ten thousand. Right? Now if a person immersed one day before the last day, that means the chances that the mikveh had become deficient up to the stage of his immersion are nine thousand nine hundred and ninety-nine out of ten thousand.

[Speaker B] Why? But the previous moment was also fifty percent, and the moment before that also fifty percent, and all those fifty-percent chances accumulated until that final moment.

[Rabbi Michael Abraham] Listen, the day before is nine thousand nine hundred and ninety-eight out of ten thousand. The day before that is nine thousand nine hundred and ninety-seven out of ten thousand.

[Speaker B] But why? Earlier too they didn’t know; it could be that it had been deficient for a long time, from the very first second.

[Rabbi Michael Abraham] You keep repeating that they don’t know. So what if they don’t know? Every problem in probability is when you don’t know. Always. So what? What does it mean that they don’t know?

[Speaker B] It means that if this were a health matter, I’d use common sense and say fifty percent, and not say anything else.

[Rabbi Michael Abraham] I don’t know—don’t tell me your office hours. I’m not coming there. What do you mean? The fact that you don’t know—sorry that I’m, yes. Just a joke. But I’m saying: the moment I have ten thousand days in which this could happen, and in each of them the probability is equal—fifty percent, fifty percent—

[Speaker B] Certainly. After all, it could absolutely be that for all the earlier moments, if someone had checked it, the answer would have been: invalid. It absolutely could be. To the same degree the probability of that is exactly equal—fifty percent every second—and that also accumulates to fifty percent over all the days.

[Rabbi Michael Abraham] I don’t know how to explain it better than that. I don’t know how to explain it better than that. Okay, fine, I just apparently can’t explain it. Okay, so in the end the claim is that what solves the problem of why we do not follow the majority along the time axis is the rule of fixed status. Since the moments are situated on the time axis, I can’t say that I’m asking whether this moment belongs to the majority of moments or the minority, because I’m asking what this moment is. I’m not asking which group of moments it belongs to, but which moment this is, because that’s the one I am addressing. Not a moment that separated from a group and each group casts its side upon it, right, like we discussed in previous sessions. And because of that, we have the rule of fixed status here, and it is treated as half-and-half. And this explanation assumes my explanation of the rule of fixed status, not Oren’s explanation of the rule of fixed status. Now, the Talmud in tractate Ketubot, which brings this law, this discussion of an open entrance, it turns out that the Rashash in his novellae on that page asks this question—let’s see it there. “But it is difficult for me: why should we not follow, in the case of a priest’s wife, the majority of the time that passed before she became betrothed? As with coins found on the Temple Mount, they are always ordinary money even during the festival season,” a Mishnah in tractate Shekalim, “for we follow the majority of the year.” Yes, there is a Mishnah in tractate Shekalim that says: what happens if someone finds coins, yes, money, on the Temple Mount? If it is during the festival season, then most likely it is money of second tithe, because then people come up to Jerusalem on pilgrimage, and at that opportunity they also bring with them the second tithe, which they are obligated to spend and eat in Jerusalem. But if it is an ordinary day, not a festival but a weekday, then most likely it is not second-tithe money but ordinary coins. And the Talmud says there that even—well, that is how it should have been—there the Talmud says that even if I found it during the festival season, I may assume that it is ordinary money and not second-tithe money. Why? The Talmud says—it’s in Pesachim, I think—the Talmud explains: “for we follow the majority of the year.” We follow the majority of the year; most of the year is weekdays and not festivals, and therefore I assume that these coins are from the rest of the year and not from festival days. So you see that we also follow the majority on the time axis. Likewise, he says, with the case of a priest’s wife who had relations and your doubt is whether she had relations after the betrothal or before the betrothal. In that situation, why shouldn’t we follow the majority of the time that was before the betrothal? That is exactly the question. He brings another example as well: “Likewise it is difficult in tractate Niddah, at the beginning of the chapter ‘The Woman,’ concerning three women who wore one cloak, that we should go after the one who wore it for a longer period than her companions.” Three women wore one garment, and we find blood on that garment, so all of them are presumed impure. We don’t know from which one the blood came out, so all of them are presumed impure. Now the Rashash asks: why indeed do we rule that way? Why not say that the woman who wore it for the longest time is probably the woman who left the blood on it, and therefore she is the one who should be impure, and the other two should not need to worry? “And similarly in many places,” yes, and in many other places. “And although one can reject the proof from that case in Shekalim”—from the Mishnah in Shekalim one could reject the proof from there, the proof that on the time axis too we follow the majority—yes, he has two proofs: the Mishnah in Shekalim and the women who wore the cloak. He says the proof can be rejected from the Mishnah in Shekalim. Why? “For there, if one combines all the ordinary money of the whole year, it will be more than the second-tithe money of the festivals and of the whole year.” In any case, the reasoning itself is sound: that we should follow the majority of the time, and in cases of majority versus proximity we follow the majority, and see Pesachim. Rabbi? Yes.

[Speaker E] In the case of Shekalim, that’s not really a majority of time. Time isn’t what causes the prohibition. There’s the status of second tithe and the status of ordinary money. It’s a majority of coins, not a majority of time in which the coins are ordinary, and so on.

[Rabbi Michael Abraham] That’s what he says. Therefore he says that from Shekalim there is no proof. Why? He says, “And although the proof can be rejected from that case in Shekalim,” because there one can say, “for there, if you combine all the ordinary money of the whole year”—think about all the coins lost in Jerusalem over the course of the year. The fact that you found it on the festival doesn’t mean it was lost on the festival. It may have been lost a week ago or a month ago, and you found it now. Therefore, among the coins that we find, most of the coins are coins that were lost on weekdays, not coins that were lost on the festival, even if the finding itself took place on the festival. Therefore you can’t follow the majority of time, because in fact, as you said, this isn’t about a majority and minority of time but a majority and minority of coins, not of time. And as for a majority and minority of coins, obviously the coins lost on weekdays are the majority, or the coins that are not second tithe but ordinary money are the majority, when you look at the whole year. The fact that you found it on the festival doesn’t mean it was lost on the festival—that’s the claim. But there is the case of the women who wore the cloak, and there apparently it is a proof. And besides, he says, the reasoning also points that way: why not follow the majority of the time, as we always do, follow the majority? Why not also here, in the case of the open entrance, follow the majority of the time? That is basically his question. Now let’s take a moment and see. I proposed an explanation earlier. The explanation for why we do not follow the majority on the time axis is that the rule of fixed status applies here. The moment is essentially standing on the time axis, it is in its place, and because of that there is no separation, no distinct sides, everything I explained earlier, and therefore the rule of fixed status applies here and it is half-and-half. If so, then now I need to check how this fits with the two examples brought by the Rashash. He brings from these examples proof that we do follow the majority, and he challenges the case of the open entrance. Now I explained the open entrance—because in terms of plain reasoning he says that the open entrance really contradicts the reasoning, whereas those examples fit the reasoning. But now we are in the opposite situation. I explained the open entrance precisely by the reasoning of fixed status—that it is fixed, and therefore half-and-half. If so, now I need to examine the two examples he brought: why there do we follow the majority? Why is that not fixed status? So let’s see. First of all, the example of the coins in Jerusalem. The claim basically is that it is, as the Rashash himself says, that we are talking about a majority of coins, not a majority of moments in time. Among the coins there is a majority that are not second tithe, an ordinary majority. You could maybe even say more than that. The coins here are really very similar to a piece of meat that separated from the stores, right? Basically the coins fell out of someone’s pocket, from his wallet. There were other coins in his wallet. Now the question is: what was the source of these coins? Was this a wallet of second-tithe money—which people usually keep separately, since one has to treat it with sanctity—or was it a wallet of ordinary money? So this is really just like a piece of meat that separated from among the stores. And therefore, if I say that most of the wallets circulating here over the time axis were wallets containing ordinary money and not second-tithe money, then as for the money I found—what difference does it make that I found it during the festival? The money I found is likely—well, not “likely,” it’s a present majority—that it separated from wallets of ordinary money, and therefore I follow the majority. This is not at all a question of majority on the time axis; it is a question of which wallets this money came from. It is true that there is a time axis here in the sense that if the money had been—if I knew that the money was lost during the festival, then I would say it was second-tithe money, and if I knew it was lost on a weekday then I would say it was ordinary money. But it isn’t the time, as Eliav’s comment earlier noted, time is not what causes the law here. It’s just that at that time there are more wallets with second-tithe money, and at the other time there are more wallets with ordinary money. So here time is not the determining factor; this is not like the mikveh or the open entrance, where my doubt really is about at which moment in time it happened. Here my doubt is not about at which moment in time it happened. If I knew it happened at a festival moment, I could resolve the question. If I knew the moment was an ordinary weekday, I could also resolve the question. But when I don’t know, the question that interests me is not when it happened but from which wallet it came. The question is that if I knew the moment in time, that would help me know from which wallet it came. But still I would decide not because of the moment in time, but because at that moment in time most wallets were either ordinary-money wallets or second-tithe wallets. Therefore the question here is not on the time axis at all. That is basically what lies behind the Rashash’s own answer. I’m just saying that the explanation in terms of two sides and fixed status of course also fits this matter. So in the open entrance and in the mikveh there really is the rule of fixed status, and therefore we do not follow the majority on the time axis. Here the doubt is not about the time axis at all, so this is not a question of fixed status versus separated status; rather here we follow the wallets, and with wallets the rule is: whatever separated, separated from the majority.

[Speaker C] And why not also introduce a factor that says it isn’t likely that a coin would lie there for two weeks without being found, and it’s much more reasonable to think that the person who found it found it just as the coin had fallen now? That seems much more logical.

[Rabbi Michael Abraham] If there really were such a consideration, it could be that it would change the law. For example, if I found this coin in a central area and in a conspicuous place where a lot of people pass by, then it may very well be that the law would be different. Because there it is not likely that it stayed there for a long time; someone would already have seen it and taken it, and therefore it probably fell only very recently. But if we are talking about a coin where I have no indication whatsoever when it fell—it could be now, it could be at some point during the year—then the law of the Mishnah is a correct law. Meaning, I am making a small interpretive qualification to the Mishnah, but it is a reasonable qualification. It doesn’t seem problematic to me.

[Speaker E] And here, is this a present majority?

[Rabbi Michael Abraham] I think so, because you are right that it’s not literally standing before us—it’s not like the stores—but the idea here is the idea I explained regarding a present majority. It’s not a law of nature, but there is a reality in this place that most of the people moving around in this place are people with wallets of ordinary money.

[Speaker E] So then it is a probabilistic majority?

[Rabbi Michael Abraham] What? No, no, because I don’t know how coins fall from a wallet of ordinary money or from a wallet of second tithe, just as with pieces of meat in stores. I don’t know how they separate. The decision is a decision by force of ignorance, not by force of statistics. But with a present majority I have “incline after the many,” which tells me that I still follow the majority, so here too I follow the majority of the wallets. This is exactly parallel to a piece of meat that separated from the stores.

[Speaker E] You are claiming that here too there is the ignorance and uncertainty about the fall?

[Rabbi Michael Abraham] Yes, it’s exactly the same thing. In meat separating from a store, after all, the meat didn’t separate from the store—the meat fell from the basket of the person who bought it in the store. So it’s exactly like falling from the wallet. Okay. Fine. So that is regarding the Mishnah in Shekalim. The second example is a Mishnah in tractate Niddah, and there it speaks about three women who wore the same cloak, yes, the same garment, and blood was found on it. Okay? Now what happens there? The claim there is that all of them basically must be impure, and the question is why not render impure only the one who wore the cloak for the longest time?

[Speaker E] Because then, simply, the longest time is not the reason there would be blood on the garment, because even if she wore the garment for only one minute, there could still be blood.

[Rabbi Michael Abraham] Exactly. Here it is simply a mistake to treat this as a majority on the time axis; it is not relevant at all. Because the question—suppose a woman wears the garment—it is not that the blood coming from that woman is a statistical event and now the question is at what moment it happened. If the woman is impure, then blood comes from her. It isn’t statistical; that’s how it is—blood comes from an impure woman. The whole question is which of the three women was impure. If the woman who wore the cloak for a short time was impure, then she would render the garment impure with exactly the same probability as if the woman who wore it for a long time was impure. There is no difference whatsoever. The question is who the impure woman is, not at what moment the blood chose to come out. And therefore it is simply not relevant. Now look, these are very important points. I bring these examples so that you see how subtle these laws, these considerations, can be. On the face of it, it all looks terribly similar. In all these cases it seems to be a question of majority over the time axis, and suddenly we discover—not at all. In the mikveh yes, in the open entrance maybe yes, in the two examples the Rashash brings absolutely not. These are not questions of majority on the time axis at all. And therefore one must be very—yes, anyone who has studied prohibitions and permissions, or majority and minority in Jewish law, knows that it depends very much, it is very sensitive to the question of what question we are asking. What exactly is the question we are asking? And one must be very careful not to be hasty in our use of the laws of majority. It is very important to distinguish what question we are asking. And in truth we saw this at the beginning of the series when I spoke in statistics, say, about Bayes’ theorem, yes? There too we saw conditional probability, and there too we saw that it is very important what question is being asked. The probabilistic answer can be completely different. The halakhic answer can also be completely different. It depends very much on what question we are asking. The question we ask regarding the drop of blood is not at what moment it fell. That is not relevant. True, if I knew at what moment it fell, that would also resolve the question I am asking. Because if I knew at what hour blood dripped onto the garment, then I would say: fine, the woman wearing it at that moment is probably the impure woman. That is true. So that is only if I knew what the moment was. But you cannot say that the question I am asking is at what moment the blood came out. That is not the question I am asking. The question I am asking is: which woman did the blood come from? And therefore the probability—say each of the women, let’s say woman A and B wore the garment for one hour, and woman C wore it for ten hours. Am I now asking a statistical question here—this is really statistics now, not a scriptural decree—what is the probability that woman A is impure, woman B, or woman C? Do you understand that it is one-third? A mathematical one-third. Here what we are saying is simply a statistical mistake. The probability is fully one-third. Because if woman A was impure, then blood would come out during the hour she wore the garment. What do I care that it was only one hour and not ten hours? During that hour that she wore the garment, blood came out from her. The same applies to the second woman. If the third woman is impure, then blood comes from her during one of the ten hours she wore the garment. So what? The duration of time plays no role here whatsoever; it is not relevant. Therefore again—and again, if you look at it from the perspective of moments in time, yes? If I knew at which moment in time it happened, then yes, that would resolve my question. If I knew they began wearing the garment at seven, the second wore it at eight, and the third from nine until nine at night, twelve hours. Okay? If you told me that the blood fell onto the garment at twelve noon, then I know it was the third. Does that mean the question I am asking is at what moment the blood came out? Of course not. I am asking from which woman it came out. If I knew the moment, that would resolve the question of from which woman it came. But the question I am asking is not at what moment the blood came out, but who the woman was from whom it came. And on that issue it is one-third, one-third, one-third; that is obvious. It is exactly like what I said when I explained the rule of fixed status: when I ask whether the store in which this piece is found was kosher or not kosher, I am not interested in whether it belongs to the majority of stores or the minority. The question is whether it is kosher or not. If it is kosher, the result will be that it belongs to the majority, not that because it belongs to the majority therefore it is kosher. The same thing here. In other words, if I know the moment in time, that would resolve for me the question of whose woman it was, but the question is whose woman it was, not at what moment in time it worked. The same with the coins, yes? Also with the coins, if I knew when the coins fell, then I could do the calculation in a way that would give me an answer. But the question I am asking is not at what moment the coins fell, but what their status is—whether they are second tithe. A completely different question. The fact that time can help me resolve the question does not mean that my question is a question about time. And therefore there is no point talking about following the majority of moments in time, yes? It is simply not relevant. Okay. There is actually just a philosophical comment here. There is room to discuss my explanation regarding the rule of fixed status in moments of time, and I basically used a description as though each and every moment on the time axis sits in its place. It did not separate, and therefore the rule of fixed status applies here. Okay? Now, do I need for this to assume that time really is some kind of existing entity? Of course it is not space, it is time, it is another kind of entity, but still some sort of entity. Or is it a fiction or a form of subjective human perspective? There is such a question in philosophy. Does the answer to this halakhic question depend on that metaphysical question—whether time exists or does not exist? Seemingly I described here some kind of time in which a moment in time is located in its place. The treatment is as if time is an existing entity. Okay, I don’t think it depends on that, because in the end, fixed versus not fixed for me reflects a type of question. I am not asking whether this moment in time belongs to the majority moments or the minority moments. I am asking whether this moment preceded the immersion or did not precede the immersion. After I answer that, it will turn out that it belongs either to the majority of moments or to the minority of moments. Everything I just said can be said even if time is only a form of our perspective. This plastic, graphic description, as though we are talking about moments of time laid out somewhere and this moment in time is sitting in its place—that’s just a description. In the end, what matters to us halakhically, if I am right in my explanation, is the character of the question I am asking. Is the question I am asking a question of which group of moments in time this moment belongs to, or am I asking what this moment is? Kosher or not kosher. Kosher or not kosher meaning before the immersion or after the immersion. Okay. So therefore, the question we ask will very often determine the answer. A wise question is half an answer. If you formulate it precisely and diagnose very, very well what the question is, then it is fairly easy to see which probabilistic and/or halakhic tool is correct to use here. The art, many times, is to define very well what the question is that is being asked. Okay, so therefore I think it does not depend on the question of the existence or non-existence of the time axis. I do have halakhic proofs that Jewish law sees time as something existing, but I don’t think we need that in this description. Good. I want to move on to the next discussion. Here it was a majority in moments of time. And the discussion about majority in moments of time basically came in order to reflect the difference between the explanation I proposed for the rule of fixed status and the explanation Oren proposed for the rule of fixed status. According to Oren’s explanation of fixed status, where you need some chooser who has some reason for his choice, I think it is hard to explain the issue of why we do not follow the majority in moments of time. The rule of fixed status does not seem relevant there. But according to my explanation, it really is called for. Okay. Now I want to propose an interesting question, which is also somewhat related to the question of what question we are asking and to the application of probability to ethical or halakhic questions, if you like. And it is the following question. A few months ago there was some conversation between Roi Yuzovitz—he has that series of conversations where he meets people and talks with them about various topics in science, philosophy, faith, and so on. And he met with Eli Merzbach, a professor of statistics, now already emeritus, at Bar-Ilan. When I wrote my master’s at Bar-Ilan, I went to consult him. He was a professor of statistics. I went to consult him because I had some statistical problem. Well, he actually gave me a source that later really helped me with my problem. And in the end, when I wrote the booklet, at the beginning I was still in my cheerful yeshiva period in Bnei Brak, so I wrote there: many thanks to all the relevant parties, among them Eli Merzbach and the Holy One, blessed be He. So he told me that it had been a long time since he had been in such distinguished company. In any event, to our matter: since then we have had many arguments, because he deals a lot with providence and statistics. He wrote a book called The Logic of Fate, in which he argues that the Holy One, blessed be He, or His providence, hides behind statistics. He is basically one of the prominent holders of this approach, against which I have spoken so many times—the notion of involvement within nature. That divine involvement need not be a deviation from the laws of nature. Statistics is merely our description of how and where the Holy One, blessed be He, intervenes. And things of that sort. It may be that later in the series I’ll still touch on that, but in any case that was his approach and I disagree completely. Any divine involvement is a deviation from nature, and therefore it has nothing to do with statistics. In any case, Azri Yuzovitz did a bit of preparation with me before the conversation with Merzbach because he wanted to raise various points on which we disagree, and in the end he sent me that conversation and I found there something much more interesting than all the usual disputes of ours that are already worn out. In his book The Logic of Fate he brought a truly fascinating example. It really got me thinking; it was a truly fascinating example about an incident on an American ship. I had it on my website. An American ship that sailed from Liverpool in England to Philadelphia. At some point on the way it hit an iceberg and broke apart, and everyone had to get into the lifeboats. Everyone got into the lifeboats and it turned out there was not room for everyone; if everyone remained, the boats would sink and everyone would die. So one man got up and decided to throw several people out of the boats, out of the overloaded boats, so that the others would survive. The people he threw out, of course, drowned, but the others were saved and reached shore. When they got to shore, that man who had thrown the people into the sea was put on trial. How can you throw people into the sea and kill them? So he defended himself. He said: what do you want from me? Had I not thrown them out, we all would have died, both they and I. What’s the idea? Is that preferable? If I had not thrown them out, they would have died anyway; only if I had not thrown them out, I also would have died and so would all the others. Therefore what I did was not to kill them but to save all the rest. The alternative was that everyone would die. This is not the trolley problem and the fat man. It is more similar to conjoined twins. With conjoined twins, I essentially take one, kill him, and leave the shared heart to the other, and the claim is that if I had not removed the second, both of them would have died, and that one whom I removed would have died anyway. So in effect I killed someone who in any event would have died, and all I did was at least save the other, who would have died if I had not done so. It is very similar to this. Okay? In any event, the claim is that he says: what do you want from me? I saved some of the people; otherwise we all would have drowned, so how can you say I am a murderer? The prosecution’s argument against him was: you are right, but you cannot choose by yourself whom to throw out; you should have conducted a fair lottery. True, it is perfectly fine to throw people out and one need not commit collective suicide so that everyone dies; there is no logic in that. If five can die and the other twenty be saved, then there is no point in sending all twenty-five to their deaths. But you cannot yourself choose five who will die; you should have held a fair lottery, and whoever came up could have been thrown into the sea if he did not jump by himself. Okay? But you need to give everyone a chance, and therefore they prosecuted him not because he threw the people into the sea, but because he did not hold a lottery. The prosecution was: why didn’t you hold a lottery? Now here there are several interesting points regarding the question of lotteries, and on these matters too I do not agree with Merzbach, but I want to focus on this discussion because there in the book he brings several arguments or reasons why a lottery is not the correct solution in such situations—that is, why it is legitimate to throw out whomever I decide. Now he also says, and it also comes up in that conversation, that according to his view it is also halakhically forbidden to hold a lottery in such a situation. And I mentioned this when we talked about conjoined twins once, so I mentioned—I think in this series we haven’t talked about them yet, right, because maybe we’ll get to it later—the halakhic decisors forbid holding a lottery in a similar situation with conjoined twins. They say one must leave both to die and not hold a lottery that would bring about the death of one but save the other; in other words, they should both die. And I argued—I wrote in an article in Techumin that in my opinion one is obligated to hold a lottery, not only permitted but obligated to hold a lottery. Now Eli Merzbach goes with the halakhic decisors and assumes that in such a situation it is forbidden to hold a lottery, and he says this there in the conversation, and therefore he has some motivation to justify this matter. He says it is forbidden to hold a lottery, and therefore how can one prosecute him for not holding a lottery? Now during the course of that conversation he says—Yuzovitz basically says he was mainly impressed by reason D. He brought several reasons there, but he brought reason D’. What is reason D’? He says: after all, why does fairness require holding a lottery? In order to place the weak and the strong in the same situation, with the same chance of survival. To give everyone an equal chance. Or, if we formulate it differently—I would formulate it in a way that is more correct—this is what the lottery does. If I could divide the lives, then I would divide the lives themselves among the people. Say they had, I don’t know, a life expectancy of twenty years if they were saved. So let’s divide it—there are twenty people there, let each one live one year. That would be the truly fair solution. Except that you cannot divide the years. Whoever survives will survive fully, and whoever does not will drown now. I have no way to divide the years. So what do I do? Instead, I divide the chance of receiving the twenty years. Instead of giving each one one year out of twenty people, so each one gets one year, I give each one a one-in-twenty chance of receiving all twenty years. And whoever wins gets all twenty years. Do you understand that this is a fair alternative distribution when I cannot divide the item itself? We see this in Jewish law and in many other places too, in the case of “either buy me out or I’ll buy you out,” the Talmudic discussion of “gud or agud.” Suppose I have a courtyard—say two brothers inherited a courtyard from their father, and the courtyard is very small, four by four cubits. Now if I divide it into two parts, each one gets four by two, which is a courtyard with no use. The minimum usable size is four by four—that is the Talmud’s assumption. Two meters by two meters, yes? Two meters by one meter is not a courtyard; there is nothing to divide at all. So that means we now have joint property and no way to divide it. What should be done? What do you do in such a case? In principle, what you do in such a case is “gud or agud,” meaning you hold a lottery to determine who will pay the other half the value of the courtyard and take the whole thing. Either Reuven takes the whole courtyard and pays half its value to Shimon, or vice versa. Okay? In principle, one could also hold a different kind of lottery and that too would be fair. Simply hold a lottery over the whole courtyard with equal chances. Each one has a half chance of getting the entire courtyard. That is the same as each one having a chance of one to get half the courtyard. Instead of dividing the courtyard, I divide the chances of receiving the courtyard. And that is fine—if I cannot divide the courtyard, I divide the chances. Therefore many lotteries are lotteries whose role is to create a fair distribution, as opposed to all the myths—the religious myths—that say we make a distribution so that the Holy One, blessed be He, will determine who gets the courtyard. The lottery is supposedly a rod in the hand of the Holy One, blessed be He, through which it is revealed to whom the courtyard should really go, who deserves the courtyard. That is how people often write. Elimelech Herzberg also writes this in many places, says it in many places, that the lot is basically the way through which the Holy One, blessed be He, runs the world. In the end the most just result emerges. The one whom the Holy One, blessed be He, wants to get the courtyard will come out in the lottery. I claim that this is a misunderstanding. It is a misunderstanding not because I claim that the Holy One, blessed be He, does not stand behind statistics—that is also true. It is a misunderstanding concerning what the role of the lottery is in such a situation. After all, there is no one here who truly deserves the courtyard; we know what true justice is. True justice is that each one should receive half the courtyard. There is no one person who really deserves the courtyard and I just don’t know who he is. If there are two people fighting over the courtyard and I do not know which of them is the owner, but I know that only one of them is the owner, then you could perhaps tell me: let us hold a lottery and the Holy One, blessed be He, will ensure that the one who speaks the truth will win. Perhaps, if you believe in divine intervention, that may be so. But in our case that is not the situation. We know the truth; the truth is that each one deserves half the courtyard. That is the truth. So the lottery is not trying to determine what the truth is, who deserves the courtyard, because the truth is known. The lottery is trying to offer us a substitute for division. Instead of dividing the courtyard half and half, which is impossible in a small courtyard, we divide the chances of winning the courtyard half and half. It is the same thing: each of them has half the chances of winning the whole courtyard. So that is a fair division. In the end only one will get the whole courtyard and the other will get nothing. But the chance of each of them to get the whole courtyard is equal, so in that sense there is a fair division here. Yes, I said that “gud or agud” in the Talmud means: you take the courtyard and pay me half its value, or vice versa, and we hold a lottery to determine who is who. But I claim that if you are already holding a lottery, then you can hold a lottery over the whole courtyard even without paying half its value. As long as you divided the chances half and half, that is a fair distribution. And that is perfectly fine.

[Speaker B] Rabbi, doesn’t it feel unfair? No, since the truth is known, that each one deserves half. So the Talmud’s solution is excellent. But what the Rabbi is proposing—the outcome is very grim. One gets nothing and one gets everything. Exactly the opposite of what should be.

[Rabbi Michael Abraham] That outcome—

[Speaker B] I could have been a billionaire and it didn’t work out, so does that make this a more just world?

[Rabbi Michael Abraham] Obviously, because when you buy a lottery ticket, what are you paying for? You are paying for the chance to win, not for the win itself. After all, in the end you almost certainly will not win. So was it justified to charge you money? The answer is yes, because you pay for the chance to win, not for the win. So the chance to win has value; it is worth money. The chance to win an entire field—

[Speaker B] If that person—if that person could really sell the—if he could say, I’ll transfer it to someone else and receive something in return, then fine, but—

[Rabbi Michael Abraham] Okay, that’s a different reality.

[Speaker B] Okay, so then there’s no problem.

[Rabbi Michael Abraham] The Talmud in Makkot 5a discusses selling the woman’s or the man’s uncertain right in the ketubah. I want to sell the ketubah, but I still don’t know what will happen. If I die first, then she gets the ketubah; if I divorce her, she gets the ketubah; but if she dies first, then nothing happens, so there is no ketubah. Now the woman wants to sell the ketubah to someone. How much should that person pay her? The answer is: the value of the ketubah multiplied by the probability that she will actually collect it. Let’s say the chances of those three events are equal, then it would be two-thirds. Two-thirds of the value of the ketubah. No problem—when you sell probabilities, usually you calculate the expected value more or less, and the expected value is considered equivalent to the commodity for which you pay. So with halves, a fifty-percent chance of winning a courtyard worth a thousand dollars is worth five hundred dollars. So if you inherited five hundred dollars, that’s what you got—you got a ticket in that lottery. A ticket in that lottery is worth five hundred dollars. And that’s fine; that’s a fair division. Again, when it’s possible to divide the courtyard, then of course you divide it—why not? But if it’s impossible to divide the courtyard, then dividing by lottery is my way of dividing the courtyard. I’m simply dividing the chances of winning the courtyard. Therefore, the lottery here is not meant to reveal who the Holy One, blessed be He, wants to receive the courtyard. It is simply our way of making a fair division when the thing itself cannot be divided. So if we now return to our friends there on the ship, the role of the lottery there is to replace dividing the years of life, which is what we really should have done. The ship is about to sink, we have twenty years of life—let’s divide that among twenty people and give each one a year. If we could do such a thing, that would be the fair division. But we can’t. It’s like a courtyard that is too small to divide, a tiny courtyard. So what do we do? We divide equally and fairly the chance of winning twenty years. And therefore, as long as the division of the chances is fair, then that’s perfectly fine. That’s the division we’re making here, and it’s fair, it’s okay. That is basically the argument for why they should have held a lottery there. And therefore, the claim against that person was: why didn’t you hold a lottery? Now Mertzbach argues: but that’s not true—he did hold a lottery. After all, what happened there on the ship was that they got into a fight. That person was simply the strongest, and therefore he managed to throw overboard whomever he chose. If they had been stronger, they would have thrown him overboard. So Eli Mertzbach says: then that’s perfectly fine—nature held the lottery. You turned out stronger, right? Darwinism incarnate—Darwinism in the ethical context, when people talk about social Darwinism, right? Not scientific Darwinism. Social Darwinism is the view that says the strong have the right. If he uses his power, then that’s perfectly fine. And what stands behind this? The claim is that when the strong person uses his power, he got that power through some kind of lottery; the other person got less power in the lottery. So the lottery came out in my favor, and nature held a lottery. Why do I now need to hold a lottery with a coin? Nature already held a lottery, and the lottery came out that I’m stronger, and therefore I threw you overboard. So in fact a lottery did take place here—what’s the problem? That’s the argument there. Now at first glance this sounds terribly outrageous. What do you mean? It isn’t equal, it isn’t… What do you mean it isn’t equal? It is… But it’s not so simple. In fact it is equal. We could have drawn lots so that you’d be stronger or I’d be stronger, and in nature the lottery came out this way. That’s an equal lottery. And therefore, if in fact you’re the stronger one, you throw the weaker person overboard and remain alive—then yes, a lottery did take place here. Why is a lottery with dice or a coin toss preferable to a lottery of genes, or a natural lottery? That is basically the claim. And therefore, that person’s defense in court could have been—I don’t think he actually made this argument, but in the philosophical discussions around the issue such a rationale was raised—saying that in fact there was a lottery here.

[Speaker C] But doesn’t a lottery require the consent of both sides?

[Rabbi Michael Abraham] No. No. Why in the world would it? Let me ask you a question: what happens if, say, we decide between ourselves on a coin toss—which everyone agrees is what should have been done there—let’s say we are two people on the boat, one can be saved, and now we toss a coin to see who gets thrown into the sea and who survives. Okay? Now suppose one of the two is unwilling to do the coin toss. He doesn’t want to. He insists on staying on the ship and having both of us drown. Do I have the right to force him to do a coin toss? I think yes. Because I’m giving him a fair distribution: he has a fifty-percent chance to survive, and I have a fifty-percent chance to survive. By contrast, he is trying to force me to die for certain, together with himself.

[Speaker C] Fine, but here he didn’t ask the other people what they proposed, what form the lottery should take here.

[Rabbi Michael Abraham] What difference does the form make? As long as the probabilities are fair, why should I care about the form? If the lottery is fair, the form is not important. And consent to the very idea of a lottery isn’t needed, because you are forbidden to object to a lottery—you’ll drag all of us into the abyss. You can’t object to a lottery. So I held a fair lottery without your consent—so what? Everything is fine.

[Speaker C] But I didn’t really understand the land example. The land belongs to both of them, right? Yes. Meaning, both of them have ownership rights in it. Their dispute is only over who will receive it, but that dispute does not negate the other person’s right to get his share of that land. The dispute is only over who will physically get the land and who will pay money for the other half. Why are you saying it’s fair for one person to get everything and the other to get nothing? That’s the problem here.

[Rabbi Michael Abraham] Here you could say this: in principle, even if we held a lottery to get the land without payment, that would be a fair lottery. Because each person gets a fifty-percent chance of receiving the land. True, a person could come and say: I’m willing to do a fair lottery, but the deal is that we’ll do a fair lottery over who gets the land and pays half. Correct. And that’s also fine. Now between those two lotteries—here I do think you can’t force one side to do specifically this lottery or specifically that lottery. There has to be agreement between the parties about which of the two lotteries we’re doing, because here there really is a difference between the outcomes of the lottery. That’s fine, I have no problem with that. But in the case of the boat, that doesn’t exist.

[Speaker C] No, with the boat I’m setting that aside, because there too it’s also—I

[Rabbi Michael Abraham] I’m saying, but in the case of the boat, that doesn’t exist.

[Speaker C] No, even on the boat these are not circumstances where you can calmly come and analyze: now I’ll hold a lottery. After the fact you say that’s what he did. But here both of them have a right; there is no reason to reach a situation where—

[Rabbi Michael Abraham] Again, we’re conducting a theoretical discussion. In a theoretical discussion I don’t care right now whether their blood is boiling. I’m asking what ought to be done in such a situation. And in that sense it is similar to division by “either divide or buy out” in land. Only in the case of land, let’s say there were no option to pay—neither of them has a penny. They have no money. What can you do? They’re poor heirs, their father is Puss in Boots. Their father left them only the little plot of land and no money at all. No money. What do you do in such a case? You understand that in such a case, if they hold a fifty-fifty lottery over the land without payment—and I claim that the case of no—

[Speaker C] I understand that then, if neither one has money to pay, the fair solution would be to sell the land and split the money.

[Rabbi Michael Abraham] No—or, or we could make a fifty-fifty lottery over… there’s also no buyer for the land, okay? For the sake of discussion. We’ll hold a fifty-fifty lottery over who gets the land. That is perfectly fine. That’s the fair solution. Now in our case on the ship, it parallels that case, where no one buys the land and no one has any money. The only way to divide things fairly is to divide the chances of winning the whole pot.

[Speaker C] Fine, if you bring in all those elements, then it changes the solution.

[Rabbi Michael Abraham] No, I’m not bringing in—I’m not dealing with land. For me the land is just an example. I’m dealing with the ship. And the ship is similar to a case of land that no one is buying and no one has money for. And therefore a lottery is an obvious requirement—that there be a fair lottery, a division of the chance to win. So the person says: yes, but genetics already held a lottery with a fair distribution, and that’s all. That’s what came out. Why do we now need to toss a coin? What advantage does an artificial lottery have over a natural lottery? The main thing is that it’s a fair lottery, and then everything is fine.

[Speaker B] By the way, the whole idea—

[Speaker D] —of Queen v. Dudley and Stephens, after all, that’s what the whole idea is about. The alternative is brute force, and that’s obvious; the alternative is fairness. It’s exactly the opposite, it’s a mirror image of Darwinistic forcefulness.

[Rabbi Michael Abraham] I’m asking why. I said before that it’s outrageous. That it seems… What you’re saying now is a declaration, not a justification. It’s like if I present you with Achilles and the tortoise, and you say: yes, but obviously Achilles caught up to the tortoise. Right—but explain to me where my argument is wrong, when my argument shows that Achilles will not catch the tortoise. You can’t solve the paradox even on the semantic level just by saying what?

[Speaker D] You can’t just say “fairness”—the word fairness carries meaning within it, and the simple elementary meaning is anti-Darwinistic forcefulness. You can’t say, can you, that fairness means letting nature flow?

[Rabbi Michael Abraham] Right, not right—what are you talking about? Explain to me why it isn’t fair. I’m claiming that it is fair. A natural lottery and an artificial lottery are the same thing. Why should I care who conducts the lottery?

[Speaker D] No, but a lottery over who is strong and who is not strong, right? It’s obvious that you can define it that way, and reality is that there are strong people and weak people. Fairness means saying: we do not let the strong, let brute force, rule. That’s basic.

[Rabbi Michael Abraham] No, no. Fairness means that we follow the lottery, and a lottery can be natural or artificial—what difference does it make? Why is an artificial lottery fair, and a natural lottery… excuse me, an artificial one is fair and a natural one is not fair? Why? Again, I’m saying once more: obviously it’s outrageous, obviously it sounds unfair, but the argument is not trivial. You have to think very carefully about what is wrong with this argument. And here I say: it’s the same as any paradox. By the way, Eli Mertzbach argues that this argument is correct. In a conversation—since the conversation was ten years after he wrote the book—he said in the conversation that he wasn’t sure he still stood by that opinion, but in principle that was his position. It is true, he said: a natural lottery is like an artificial lottery; there is no difference at all. I claim he is mistaken, but I need to explain why he is mistaken. Because again, paradoxes are not solved by saying… well, obviously that’s not right. I know it’s not right; explain to me what is flawed in the argument, the argument that shows that it is right. So I’ll explain that…

[Speaker D] It fits very well: if he claims that God’s providence operates through the natural conduct of reality, then it’s very natural that Darwinism is divine providence—it’s exactly what should be, the whole thing is already here, it’s wonderful.

[Rabbi Michael Abraham] No, no, it doesn’t depend on that. Even if this lottery is conducted not by the Holy One, blessed be He, but by blind nature, as long as it gave me fifty percent, everything is fine. Why should I care whether the Holy One, blessed be He, decided it or whether it happened through who knows what, blind fate? If it gave me fifty percent, then fifty percent is fair.

[Speaker D] But why do we need fairness at all? Why fairness? Why is that a good thing?

[Rabbi Michael Abraham] All of us are assuming that fairness is necessary. I’m not going to get into moral philosophy right now. So if fairness is necessary, the only question is how to implement fairness in this case—that is the question we are asking here. Okay, I’ll stop here because this explanation takes a little time, so we’ll continue next time. Any comments or questions, if there are any? Okay, then have a peaceful Sabbath.

[Speaker C] Have a peaceful Sabbath, thank you very much.