Doubt and Statistics – Lesson 1

This transcript was produced automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.

🔗 Link to the original lecture

🔗 Link to the transcript on Sofer.AI

[Rabbi Michael Abraham] In science there’s a certain kind of confusion here among physicists, sometimes a bit among mathematicians too, but it’s mainly in physics. There’s a confusion between two types of situations. A state of doubt, in the simple sense, is a state in which I’m missing information. There is some reality before me, and I don’t have complete information about it, and so I’m in a state of doubt. I don’t know whether the full information is this way or that way; it could be that the full information is a theory, it doesn’t matter, but I’m in doubt because I don’t have the full information in hand. But the fact that I don’t have the full information in hand can stem from two different reasons.

One reason is simply that I’m not smart enough or not sufficiently equipped with information. That is, part of the information just isn’t available to me. There are various areas or various facts in the world that I don’t know; the information isn’t in my possession. Maybe it’s not even accessible to me, and maybe it’s not accessible to anyone. Fine. But still, the information exists somewhere; it just isn’t accessible to me. That’s one type of missing information.

Another type of missing information comes from what we might call epistemic doubt, cognitive doubt: doubt because my cognition does not grasp the full reality; I’m missing information. But there is also ontic doubt. Ontic doubt means—ontology is the theory of being, epistemology is the theory of knowledge—and this is doubt that stems from the fact that in reality itself the information does not fully exist. That is, even in reality there is no information. Reality itself is not sharply defined; it is vague in some way. And because of that, I too have some kind of lack of information. But here the term “lack of information” is not accurate; it’s misleading. Because “lack of information” as a term usually indicates a situation in which the information exists somewhere, it’s just not in my possession. By contrast, when I say that reality itself is vague, the claim is that the information as such does not exist. Not merely that it isn’t in my possession or accessible to me—there is no such information. That information does not exist. I’ll clarify this in a moment with examples.

You know what, I’ll start with an example that may make this a bit clearer. In Richard Taylor’s book Metaphysics—I think I’ve mentioned it several times in the past—it’s an introductory book to basic issues in metaphysics, a fairly accessible introduction, so for people who aren’t familiar with philosophy, I think it’s a very interesting book. In one of the chapters there, the book deals with fatalism. Fatalism means that the future is dictated to me in advance; it’s not in my hands, not under my control, there’s nothing to be done—what will happen must happen. It’s that kind of Druze conception: if it was decreed that I will die, then I’ll die; the bullet already has my address written on it, nothing I do will help. That’s the notion of fatalism.

Now, there is fatalism based on religion, like among the Druze or elsewhere, where the claim is basically that God runs things here, and therefore He determines what will happen; things are not in my hands. There is also fatalism unrelated to religion, which may perhaps be connected to determinism. That is, since reality proceeds deterministically, it dictates things—the present state dictates the next state, the continuation—then basically the matter is not in my hands. There’s no free choice; the matter isn’t in my hands; everything that happens is imposed on me.

Now, when Richard Taylor discusses the question of fatalism, among other things he talks there about the question of what we’re discussing—knowledge and choice. Because if the Holy One, blessed be He, knows everything in advance, what will happen, then in fact what will happen tomorrow is already dictated today. And therefore tomorrow I cannot choose to behave differently, because already today the Holy One, blessed be He, knew that I would choose this way or do this or do that. So then in effect it was already known or fixed today, right? That’s the question of knowledge and choice.

He brings there a story about some American teacher—Osmo’s story—about some American teacher in the Midwest, in a small town in the American Midwest, who one day walks into the library in his town and sees on one of the shelves a book that stands out a bit or something like that, and the title says: The Story of Osmo. And this teacher himself is named Osmo. Oh, interesting—The Story of Osmo, an interesting anecdote, let’s see what this book is. He opens the book. The book begins to describe: Osmo was born on such-and-such a day, in such-and-such a place, to these and those parents. He is stunned, because these are exactly his biographical details. It describes exactly what happened to him: where he was born, who his parents were, in what place, when, and so on.

Well, he gets curious, and it starts becoming a bit strange. He keeps reading. Osmo went to Rachel Kindergarten and then Leah Kindergarten and then pre-kindergarten and school and got such-and-such grades and had such-and-such friends and so on—in short, his entire biography appears on the following pages of this book. At a certain point in the book he reaches a situation where Osmo enters the town library there in that same town and sees a book titled The Story of Osmo; he opens the book and starts reading, and in short, it brings him up to the present moment. And this book simply contains a complete description of Osmo’s biography up to the present moment.

But the book doesn’t end; he has only reached page 119. Meaning, now there are still, I don’t know, several more pages. Not many, by the way, but a few more pages. And he’s practically shaking with fear: what now—if I open the next pages, then I’ll actually see what is going to happen to me in the future. That’s frightening. Maybe there are people who would want to know that; I’m not sure everyone would. I think there are quite a few people who would not want to know. Don’t tell me how I’m going to die, for example, right? Or things of that sort. Unless—unless it’s in my hands and I can avoid it. But if you have fatalistic information, meaning information that is certain to happen and that I have no way of dealing with, then it’s better that I not hear it. In other words, don’t tell me about it.

In any case, Osmo nevertheless opens the book, continues reading, and there it says that Osmo will die in a plane crash on the way to New York. Okay. This is on that same date, a few days later, and on that date he really was supposed to fly—but not to New York at all, rather somewhere else entirely. Fine. So Osmo boards the plane with a bit of anxiety gnawing at him, a few days later, right? He boards the plane, anxious. They take off. At some point he hears the captain announce over the intercom: Friends, there’s a storm, we’re changing course, we’re heading to New York, we’ll land there. Osmo goes into hysterics. He enters the cockpit and struggles with the pilot in order to prevent him from turning toward New York, and that struggle crashes the plane. And that’s how he dies. That’s fatalism at its best—or worst, right? It’s the appointment in Samarra, for those who know.

In any case, I want to use this story for one point. Taylor makes various things out of it in several directions; I want to ask one particular question. The fact that there is such a book in the library, containing all the information about the future, essentially means that the future is predetermined. It’s not in my hands; what will happen is already fixed today. That is, already today I know what is going to happen in the future. Now, let’s say Osmo had not read the book. Assuming the information in the book is correct, he still would have crashed on a plane on the way to New York, because that’s what the book says. The book says it, the book knows, right? So the information exists there on the shelf in the library even if Osmo never opened the book.

Of course, in the story itself, then he wouldn’t have struggled with the pilot, it would have happened differently, that’s not important, that’s just the story. But I mean on the principled level: the determination of what will happen in the future does not depend on whether Osmo opened the book or not. The very fact that there is a book in the library containing all the information about the future essentially means that already today the future is fixed, correct? I don’t need to read the book in order for that to negate my ability to choose freely tomorrow.

And more than that: no one needs to read the book. Even if no one in the world has read this book, and no one wrote it either—it just exists there in the library—still, that doesn’t really matter. As long as in this book there is correct information about what will happen in the future, that fact itself dictates the conclusion that the future is not in my hands. That is, the future is already fixed today. Whether this information is known to someone, or known to no one and simply sitting on some dusty shelf in a library, changes nothing, right? In this context it is enough that the information exists in order to tell me that tomorrow I have no free choice, no decision about what to do; it’s not in my hands. It doesn’t matter whether anyone knows this information or not.

Why am I saying this? Because there is the Or HaChaim, in Genesis chapter 6, at the end of chapter 6. He discusses the question of knowledge and choice, and he says there that God’s foreknowledge in fact negates free choice. Therefore, there is no escaping the conclusion that the Holy One, blessed be He, refrained from knowing—He shuts His eyes in order to leave us free choice. Because if He knew, that would dictate our actions. And in order to allow us to choose freely—so that the outcome of our choices would not be predetermined but would remain under our control—the Holy One, blessed be He, withheld from Himself the information about the future.

Now, as I just described, that does not solve the problem. Because what negates the possibility that I will have free choice tomorrow is the existence of the information, not the fact that someone knows it. If the book exists in the library, even if no one has ever opened it, still, if such a book exists in the library, then I have no free choice. Therefore, to say that the Holy One, blessed be He, shuts His eyes and doesn’t look at the information, doesn’t open the book, does not solve the problem. The problem does not stem from the Holy One, blessed be He, knowing the future. The problem stems from the fact that information about the future exists. Even if the Holy One, blessed be He, did not look at it and did not know it, if the information exists, then I have no free choice. Therefore, the claim that the Holy One, blessed be He, withheld from Himself knowledge does not really solve this problem of how I can have free choice—unless we say that when he says the Holy One, blessed be He, withheld Himself from knowing, what he means is that He prevented the information from existing. That is, He gave us free choice, and once the choice is free, the information cannot exist today before I perform the act of choice. Okay. But merely not looking says nothing.

Here I’m using this example so you can see the difference between ontology and epistemology. Ontology is a branch of metaphysics, the theory of being, what exists in the world. Epistemology is my cognition of the world, what I know about the world. Those are different things, different things.

So here, in the case of Osmo’s story, in the discussion I just had, the existence of the book in the library means that the information exists, meaning that reality is predetermined, even if I don’t—even if nobody knows it. But if nobody knows it, then each of us, and perhaps including the Holy One, blessed be He, is in epistemic doubt. In epistemic doubt means that the information is not in his possession or is not accessible to him, so he doesn’t know; he lacks information. But the assumption is that the information exists—the book is there in the library—I just don’t know it.

By contrast, ontic doubt means that there is no such book in the library at all. There is no book in the library. If you ask me today what so-and-so will do tomorrow in an action that depends on free choice, I should say not only that I don’t have the information—rather, there is no information. Not “I don’t have it,” but “there is no such information.” The information does not exist today at all. Reality itself is open. So-and-so can do X and can do Y. Reality does not dictate what he will do. That is ontic doubt, not epistemic doubt. And it is doubt that essentially stems from the fact that in reality itself there is not one answer to that question. It’s not just that I don’t know the answer to that question. Okay?

So I think this illustrates the distinction between ontic doubt and epistemic doubt. Now let’s look—I’ll bring you a quote from James Gleick’s book on chaos. There, just a moment, he describes the Santa Cruz group. The Santa Cruz group is basically the people who first conceptualized the notion of chaos. Later it became a very interesting field of research in both mathematics and physics. But at that time they were just beginning to conceptualize this phenomenon of chaos.

What is chaos, basically? Chaos—I’m giving a very simple and rough definition—is essentially a situation in which there is very great sensitivity to initial conditions, to the starting state. For example, if I’m standing on the second floor of a building and holding a piece of paper, and now I let it go, the air, the wind, the currents in the air will cause it to fall here, fall there. You can’t really know in advance exactly where that piece of paper will fall. That is called a chaotic situation. Okay? A chaotic situation means I have no way of predicting where this piece of paper will fall, because it depends on wind currents, on all sorts of random processes that I cannot know in advance what will happen there. That is, for example, one example of a chaotic phenomenon.

Of course, that’s a very rough definition. But for instance, if I take this piece of paper, this already comes closer to the mathematical definition of chaos: if I take the piece of paper and let it go here, it will fall in one place. If I let it go one centimeter to the side, then it will fall in a completely different place. Even though the point from which I started is very close to the previous drop I made, the result can land very far away; there is no connection. Although there is a connection between the two starting points, the endpoints are unrelated. That is, the two endpoints may be entirely unrelated to each other. That characterizes chaotic situations, because they are very sensitive to initial conditions. It basically means that if I started here or a millimeter to the side, the result can be very, very different. Okay? That is called sensitivity to initial conditions. That is what characterizes chaotic situations.

Now what happens in chaotic situations is that I have no way of predicting the result. You understand that if being in a certain environment dictates where it will fall, and if I change things a bit and then below it also changes only a bit, the place where it falls changes only a bit—or there is a simple relationship between the change at the beginning and the change at the end—then it is relatively easy to calculate the path from the start to the finish. You can predict it. But in a place where there is no relationship between the beginning and the end, then you cannot predict.

Take, for example, an extreme case. I take this piece of paper. Now in principle, if I know all the winds and everything, then I can predict where it will fall. But since I cannot know exactly where I released it—whether I released it here or a millimeter to the side—and that can greatly change the place where it falls, then because of this sensitivity to initial conditions, in practice I have no way of predicting where it will fall, because I cannot know exactly where I released it. There is always some limit to the resolution of that measurement. How do I know exactly where I released it—whether it was here or a millimeter to the side? I can’t know. Or a thousandth of a millimeter to the side, or a micron to the side. Therefore I have no way of knowing where this piece of paper will fall. That’s the one-foot summary of the phenomenon of chaos.

About this, one of the early chaos theorists, David Farmer, writes the following. He says: “On the philosophical level, this seemed to me like a practical way of defining free will, in a way that allows you…”—to reconcile “permission is granted” with “everything is foreseen.” Yes, meaning: the system is deterministic, but you can’t say what it will do in the next moment. There is one coin with two sides here. Here there is order out of which randomness emerges, and one step away there is randomness with order underlying it.

He is basically very excited by this phenomenon because the behavior looks completely random. I have no way of predicting what will happen. But in fact there is no random component here at all. Everything is really—this is an entirely deterministic process. Yes, think about this paper that I drop from the second floor, this piece of paper. In principle it is a completely deterministic process; there is nothing random there. If you give me the directions of the wind and its strength and the density of the air and the exact point and exact angle at which I released this piece of paper, then in principle there is a calculation that will tell me where this paper will fall. It’s just a very, very complicated calculation and one that depends very strongly on the initial conditions. In principle there is nothing here that is random. This is all terribly deterministic, and nevertheless I cannot predict where this thing will fall—which is seemingly a contradiction. If it is deterministic, then I can do the calculation and know what the result will be. But no: even though it is deterministic, I have no practical possibility of doing the calculation and knowing what the result will be.

That’s what so impressed Farmer, and all those people there. And therefore he claims that there is here some sort of solution to the problem of “everything is foreseen, yet permission is granted.” Because basically within a physical world that ostensibly—and we too are physical creatures, human beings—then ostensibly everything is governed by the laws of nature or defined by the laws of nature. So the matter is entirely deterministic. Then how does a person have free choice? Seemingly he doesn’t. If you adopt the deterministic picture, then there is no free choice. But no: here we have found certain domains or certain phenomena in which, even though the behavior is deterministic and governed by rigid laws, it is still impossible to predict the outcome. So here we have a mathematical or scientific solution to the problem of free choice, and why it does not contradict the deterministic picture of the laws of physics, the laws of nature. That is his claim.

Where is the mistake? The mistake is of course that he identifies two things that must not be identified. By the way, it’s really a mistake about the meaning of correlations, which I talked about at the end of the previous series. He identifies free choice with inability to predict the result. Once I arrive at a situation where I have no way to predict the result, then that is essentially a situation that can be used as a model for free choice. In other words, for him, when I cannot predict the result, that is equivalent to a state of free choice.

But that is of course not correct. It is true that if I act in a libertarian way, if I have non-deterministic free choice, then there is no way to predict the result. But it is not true that if there is no way to predict the result, that means there is something libertarian here. Here the field of chaos shows us that although you cannot predict the result, it is clear that this is a situation that is entirely deterministic. There are well-defined laws of nature that explain it, that show you in principle that it leads to a predetermined result. Because of difficulties of computation, the amount of information you have, and so on, you do not know how to do this calculation. But in principle such a calculation exists; you just don’t know how to do it. Therefore, what we have here is epistemic doubt and not ontic doubt.

When I’m asked where this piece of paper will fall, it’s not that in reality itself it is not defined where it will fall. It is completely defined. If I knew everything, and knew all the laws and all the information and everything, I would know how to tell you exactly where this piece will fall. Why don’t I know how to tell you that? Because not all the information is in my possession; I am missing information. So in fact this is epistemic doubt and not ontic doubt. Okay?

In free choice, as I discussed earlier regarding God’s knowledge and human choice, free choice means that in reality itself the result is not unambiguously defined. There is not one result in reality itself; reality itself allows two different results or several results. Therefore there, the reason I cannot say what the result will be is because there is no result. The problem is not an epistemic problem, a cognitive one—how much I know about reality. The problem is in reality itself. Reality itself is not uniquely defined. Therefore this is ontic doubt and not epistemic doubt.

Now what I basically want to claim is that chaos describes epistemic doubts: human inability, or lack of information, which prevents us from carrying out the deterministic calculation to the end. But there is such a calculation. In principle, someone who has in hand—the Holy One, blessed be He—who has all the information and all the computational power, infinite computational power, would be able to tell me exactly where the piece of paper will fall. And by the way, for that He would not need any prophecy. He does not need prophecy in order to see where the piece of paper will fall. He needs to perform the calculation. The calculation will tell Him where it will fall; there is no need to try to foresee the future. He has to look well at the present, perform the calculation, and reach the conclusion. Why? Because from the standpoint of reality itself there is one determinate outcome here; it is dictated by the laws of physics. When I, or Farmer, do not know how to say it, that is because of our limitation. Because we do not possess all the information. But the Holy One, blessed be He, does have all the information, and therefore He can perform the calculation.

As an example, this reminds me of a Rashi on the portion of Shemot, on the verse: “He turned this way and that way, and saw that there was no man; so he struck the Egyptian and hid him in the sand.” Rashi brings there a midrash, where the midrash says that “he saw that there was no man” means that no person who would convert was destined to come from this Egyptian, and therefore he killed him; that Egyptian was killed on account of his end.

Now what does this actually mean? This prophecy—that no person who would convert would descend from this Egyptian—to give you that prophecy you don’t need to be Moses our teacher. I can do that too. Why? Because in another moment he is going to kill him—so how will anyone come from him? Moses our teacher did not prophesy the future; Moses our teacher determined the future. The moment he killed the Egyptian, obviously no one would be born from him. So I ask myself, wait, let’s try to think what will happen in the future. What do you mean, what will happen in the future? What you yourself are about to cause with your own hands—that is what determines what will happen in the future. You are about to kill him, so of course he will have no descendants at all, and certainly no descendants who will convert.

But this is not because you know how to foresee the future. Your present action dictated what would happen in the future. Therefore when Moses our teacher turned this way and that way—yes, he saw that no one who would convert was destined to come from this Egyptian—that was not contemplation of the future. It was contemplation of the present. He was basically asking himself: under the hypothetical assumption that I leave him alive, what will come of this fellow? Can anything positive come from him? Assuming conversion is positive. So he told himself: no, nothing positive can come from him. Which means that he was actually discussing the question of the Egyptian’s state in the present, right now. In light of what I see now in this Egyptian, what do I estimate will come from him in the future? This is not a question of foreseeing the future.

I am not trying to look at the future and pull that future information toward me as if I have some ability to view that future information and draw it in. We are not dealing with future information. That future is an imaginary future. Because this Egyptian will not remain alive in order to have descendants whose conversion or non-conversion I could then examine. I am about to kill him, and thereby I determine the result that he will have no descendants. So you don’t have to be a great prophet to say that no one who would convert will come from him. I determined that with my own hands; no need for foresight of the future.

Therefore it is clear that what Moses our teacher saw here, he saw in the present, not in the future. He says: a person with such a psychological makeup, spiritual makeup, whatever, it cannot be that something positive will come from him, and therefore he killed him. The future here is an indication of the Egyptian’s present condition. But the decision to kill him was a decision based on his present condition, where the indication is: from someone who looks like this, what good can possibly come? Therefore, for example, if we adopt the libertarian assumption that every person has free choice, it could be that Moses our teacher was mistaken. It could be that if he had left him alive, and the Egyptian had chosen good, or his sons had chosen good, then they would indeed have become good people or indeed have converted. A convert and a good person are not the same thing, but just for the sake of discussion. And that does not contradict the fact, the reasoning, that Moses our teacher employed, because Moses our teacher was not considering what really would happen in the end. Moses our teacher did not judge him on account of his future; Moses our teacher judged him on the basis of his present condition.

[Speaker D] Rabbi, isn’t there a very sharp criticism here by Rashi of Moses our teacher? After all, he didn’t exchange a word with him, didn’t speak to him, he saw one terrible deed that he was doing, and on that basis he ruled against him.

[Rabbi Michael Abraham] Don’t get me now into interpretive questions about this midrash of Rashi. I’m using it as an illustration to show the difference between lack of information and a reality that itself is not fixed. What I want to say is that Moses our teacher looked at the present, but he determined the future with his own hands. Therefore it doesn’t contradict the fact that a person essentially has free choice. Is it justified or not justified? And how does it fit with the midrash about Ishmael—“where he is”—and the stubborn and rebellious son and the pursuer? You can debate this endlessly. That’s for the next Sheva Berakhot; we can think of what little homilies to say about it.

[Speaker C] So what’s the idea behind looking ahead into the future? What is he looking for? I don’t understand. What is there for him to look at if he is now determining what is going to happen?

[Rabbi Michael Abraham] Looking ahead into the future means looking at his present. Trying to analyze his personality and see what will come out of it.

[Speaker C] Meaning, he now looks at him and can know what will come from him without looking into the future?

[Rabbi Michael Abraham] No, it’s a hypothetical question about a hypothetical future. If I leave him alive, what do I expect will come out of this fellow?

[Speaker C] And how would I know that?

[Rabbi Michael Abraham] Fine, so he knew. He had some ability to look at the present. I don’t care—he knew. He had that ability. What difference does it make where he knew it from?

[Speaker C] But it sounds like he was looking into the future and not looking at the present. A person is now in whatever state he is in now—how can a person know?

[Rabbi Michael Abraham] This never happened and was never created, so what is there to discuss? It’s aggadic literature. This midrash is trying to tell us something, to say something. I don’t care right now whether Moses our teacher had those abilities or not. I’m assuming he did, and now I’m asking: what does that mean?

[Speaker C] And you interpret it as meaning that he wasn’t looking into the future, and I’m having a hard time understanding that.

[Rabbi Michael Abraham] It’s obvious he wasn’t looking into the future. Because if he had been looking into the future, then obviously no one would come from him, because you are killing him, so the future is dictated by that. The fact that he was not looking into the future is a fact. He cannot look into the future. He determined the future. Meaning, if the action now is determined on the basis of what will happen in the future—not on the basis of what is supposed to happen in the future—then he doesn’t need to look at anything, he simply needs to kill him and that’s it. The moment he killed him, whether he was righteous or wicked, no one who would convert would come from him. Correct? Because if he is dead, then he won’t father anyone. There’s no need to look at anything. If he looked, then apparently he looked at the present and not the future.

[Speaker C] And all God’s promises, when He says, “you will leave with great wealth,” and all kinds of things like that? I don’t understand. When the Holy One, blessed be He, determines things that will happen in the future, and it’s not connected to anyone’s choice, that’s what is going to happen.

[Rabbi Michael Abraham] So it could be that He took away people’s choice and dictated the future. What’s the question? I don’t understand.

[Speaker C] The only time the Holy One, blessed be He, took away choice was with Pharaoh, as far as I know. Who said that? Because there God said it explicitly, that He would harden his heart.

[Rabbi Michael Abraham] Wow—what an Olympic logical leap you just made. The only time the Holy One, blessed be He, took away choice was only with Pharaoh—why? Because there it’s written explicitly. So what? If there are places where it isn’t written explicitly and it still happened, why not?

[Speaker C] So all those decades in Egypt, all the people who were there, hundreds of thousands of people, they had almost no free choice so that the whole story of Egypt would unfold as the Holy One, blessed be He, promised Abraham?

[Rabbi Michael Abraham] They didn’t have choice at those specific points where they were needed in order to unfold the story of the Exodus from Egypt. Very well. What’s the problem? There are situations in which the Holy One, blessed be He, takes the reins into His own hands.

[Speaker C] So does a person have free choice or not? Or does he have free choice subject to…?

[Rabbi Michael Abraham] He has free choice in those places where he has it, and there are places where he does not have free choice. And sometimes the Holy One, blessed be He, can take a person’s free choice away regarding certain issues or certain points. There is no problem with that. He gave me choice; He can also take it away. Even without reference to the Holy One, blessed be He—do I have free choice whether to fly or not? No. There are things that are not in my hands. What can you do? So if the Holy One, blessed be He, takes still more things that were in my hands and turns them into things that are not in my hands, then regarding those things too I now have no free choice. Nothing happened. I don’t see any problem with that.

[Speaker C] You don’t see any problem with the Holy One, blessed be He, regulating people’s free choice in the world according to various things? Then free choice is not real free choice; it’s partial.

[Rabbi Michael Abraham] Do you have any doubt that He does that? What does that have to do with me now? What, can you choose anything you want? I can’t. There are limitations. There are things I can’t do. I have no choice to fly, as I said before. There are things that I…

[Speaker C] Yes, but in physical matters. But in the mental realm…

[Rabbi Michael Abraham] Let’s go back to Rabbi Dessler. No, I don’t.

[Speaker C] I’m not talking about physical constraints. Fine, not physical constraints, physical constraints.

[Rabbi Michael Abraham] Does that matter? There are mental constraints too, not only physical ones. The mental realm also has constraints. Now, can every person reach infinitely many mental abilities? I don’t agree. There is no indication of that whatsoever. Why on earth? We are limited mentally as well, not just physically. Obviously. What kind of question is that? Meaning, an impulse—

[Speaker C] —that cannot be overcome.

[Rabbi Michael Abraham] An impulse that cannot be overcome is a state in which the person was not free to make a decision about his action. That’s a mental constraint, not a physical constraint.

[Speaker C] But it’s still he…

[Rabbi Michael Abraham] We don’t want to get into discussions of the topic of free choice; it’s not connected to this. I’m only using this example to clarify the difference between the epistemic and the ontic. Okay? Meaning, the question whether reality itself is open or not open, as opposed to the question of what I know about reality itself. Those are two completely different things.

So I return to our line of thought. Basically I want to define two situations of incomplete information that a person has. Two situations that can both be called doubt. One type of doubt is epistemic doubt. That is, the information exists in the world, but not all of it is in my possession, and therefore I’m in doubt because I lack information. And there are situations in which in the world itself the information is not unambiguous. That is, reality itself is not fully fixed.

Now the question is: how can there be such a situation of ontic vagueness? Because if you think for a moment about all the examples—let’s say I ask you: give me examples of situations in which reality behaves randomly. I assume the examples you would raise would be rolling a die, tossing a coin, things of that kind. But if you look at those situations of rolling a die and tossing a coin, you’ll quickly see that there is nothing random there at all, as I said before. If you toss the coin or the die, tell me the initial speed and the angle at which you release the thing, the air friction, the winds, the height from the floor—give me all those data, and in principle I can tell you on which face the die will land or on which side the coin will land. There is nothing random here. There is only computational complexity, or complication. But there is nothing here that is really open in reality itself. Therefore in fact both rolling a die and tossing a coin are entirely deterministic processes. There is nothing random there. Newton’s second law is, in principle, the tool for calculating the result there. Completely deterministic. Except what? We don’t know how to do that calculation. So we use statistics to deal with the situation. But that is not because something random is really happening there. Nothing random is happening. Everything is deterministic.

Now, if rolling a die and tossing a coin are like that, what isn’t like that? Everything you can think of on earth is like that. In fact everything in the world proceeds according to the laws of physics. Everything in the world is deterministic. There are things that are complicated, and therefore I don’t know how to calculate what will come out. But that doesn’t change the principle; it’s just a problem on my end, an epistemic problem. But on the ontic, metaphysical level, in the world itself, everything is dictated; everything is foreseen.

[Speaker D] Everything is foreseen, except a person’s free choice—if one believes in that.

[Rabbi Michael Abraham] Yes, fine, okay, free choice—true, if one believes in that. But I’m talking about something from our everyday experience. Try to think of something from our everyday experience, and you’ll see that everything you treat as something random is not really random. Meteorological processes—will it rain in a month? Today we don’t know how to predict what will happen with rain in a month, right? That’s beyond the predictive range of meteorology today, at least. Okay? But is that really open? Or is it only a computational difficulty? It’s pretty clear—at least according to standard physics today—that it’s only a computational difficulty. That is, in principle, if you give me all the data and a computer with infinite computational power, I could tell you whether it will rain even ten thousand years from now.

[Speaker C] That’s if there is no choice.

[Rabbi Michael Abraham] Yes, yes, I’m talking about natural processes at the moment.

[Speaker C] No, I mean if human beings have no choice.

[Rabbi Michael Abraham] I’m saying I’m speaking about natural processes. Natural processes are unrelated to human choice.

[Speaker C] No, it is related, because we behave and we create things that affect the weather.

[Rabbi Michael Abraham] Yes, therefore I’m saying: a process that is entirely natural, without human involvement, okay? Hypothetically, of course. Human beings always somehow affect things. But—or at least even if human beings affect things, then human free choices have to affect them, not just the fact that humans affect them. That’s not enough, because then it would still be deterministic. Rather, events of human choice would have to affect them. But yes, in principle it can affect almost anywhere.

So the claim is that everything you try to think of is in fact not truly random. And if we deal with it using probabilistic or statistical tools, that simply fills some gap in the information. I’m missing information or computational power, but it does not really express any freedom in reality itself. The laws of physics say this. Because the laws of physics say that everything that happens has a deterministic cause that produces it, in every field. And consequently also in biology and chemistry and anything else you want—at least in the accepted reductionist perspective.

The only exception to this is quantum theory. Now I don’t want to get into details, but in quantum theory all the distributions, the lack of understanding, and the confusions and perplexities there are basically rooted in this point. Quantum theory presents us with a reality we have not encountered in any other field of science or of life. And that is the reality of genuine ontic randomness, not epistemic randomness. That, in a nutshell, is the uniqueness of quantum theory—or at least of the accepted interpretations. There is some debate about it, but in the accepted interpretations the uniqueness of quantum theory is that it contains phenomena of freedom in reality itself, not merely lack of information on our part. Yes—for example, the double-slit experiment.

[Speaker B] Yes, maybe if you’d like, we can see it. Here, from this site, I’m taking this thing.

[Rabbi Michael Abraham] Look here: when you shoot an electron, okay, through a hole—a screen, there is a screen here and it has a hole in it, a slit. Okay? We fire the electron, and then the electron hits here. Or if the slit has a certain width, then it will hit in these regions. Fine? The intensity of the impact will look something like this. Let’s say this graph describes what will appear here. Here there is photographic film, so if the electron hits the film it leaves a mark. I send electrons, and I see that the distribution will be something like this. Fine? That’s what will happen with light too, and that’s what will happen with electrons too.

What happens when there are two slits? Yes, now we have two slits. This is one slit, this is the screen, we have two slits, one slit and a second slit, and here is the photographic film and this is the graph. Okay? So in principle, when I do a two-slit experiment and send a beam of particles, some will go through this slit and create this hump, and some will go through that slit and create that hump. Right? The maximum is at the center of the slit, and here too the maximum is at the center of the slit. Okay? That’s a beam of particles.

[Speaker C] Excuse me, is that all particles or only particles of light?

[Rabbi Michael Abraham] No, no. I’m talking about the opposite, not particles of light. A beam of particles, electrons. Okay? By contrast, if I send light—and for the moment I’m not even saying it’s particles—I send light, then you get a picture like this. There’s something here, there’s something here, and here in the middle there’s constructive interference. A wave phenomenon. Light is a wave, so there’s a wave phenomenon in the middle: even though it’s not opposite either of the slits, there’s some kind of maximum impact here. Because the wave coming from the right and the wave coming from the left somehow reinforce each other in the middle. I’m putting this very simplistically, because there are requirements regarding the distance between the slits and the wavelength, but I’m not getting into the details right now. That’s what you see with light. Now, surprisingly, it turns out—and this is within quantum theory—that even when I send a beam of particles in this way, I get this picture. I would have expected that with a beam—a beam of particles—the picture would be this one. But no, you get this picture, just like with light. And the conclusion is basically that the electron itself is also some kind of wave and not a particle. Awful, yes—forgive me for the crudeness of the description—but I’m doing only what we need in order to understand the discussion here. The even more amazing thing is that when we send one electron, not a beam of electrons—one electron—and there are two slits here, the picture that results is this one. If I put a detector next to this slit, one that tells me whether the electron passed here or didn’t pass here, then if the detector goes off, that means the electron passed here. If the detector doesn’t go off, then the electron passed here. So I’ll get either this lobe, yes, this lobe, or this lobe. And that’s what I would expect. But if there are no detectors next to the slits, then I get this picture, just like light. Really like a shore, as Netanyahu Natan says. Okay? So the particle behaves like a wave. In the accepted interpretation, this basically means that unlike the regular conception of particles, where I say: if I sent a particle toward this screen and it reached the photographic plate, then either it passed through this slit or it passed through this slit. Right? It could be that I don’t know which slit it passed through. So I don’t know; then I have a doubt whether it passed here or passed here, and that’s an epistemic doubt. Because I don’t know. It passed through one of the slits, obviously; I just don’t know through which of the two slits it passed. And that’s an epistemic doubt. But quantum theory says that’s not how it is. The particle itself—part of it passed through this slit and part of it passed through this slit, or it passed through both here and here. It’s not that I don’t know; in reality itself it passed through both slits. But what does that mean? It’s only one particle, not two particles. How did it pass through both slits if it’s one particle? The answer is that the state of the particle is built in such a way that it’s as if—it’s called a superposition, or a sum of states—one state is a pure particle passing through this slit, one state is a pure particle passing through this slit, and the real state, if I didn’t put a detector there, is actually the sum of the two states. I sent one particle, but it was in a state in which it passes through this slit plus a state in which it passes through this slit. And therefore the picture from the one particle also looks like this. It’s as if it passed in two particles. More than that: it even interferes with itself. There’s the middle lobe. Not only do I see from one particle two hills, both opposite this slit and opposite this slit, but I also see the interference. Interference means that what passed through this slit joins with what passed through this slit; they reinforce each other. That’s called constructive interference, and they create here some kind of radiation intensity—intensity, yes—on the photographic plate, a high intensity of the radiation that was absorbed there. Okay? Now this is a very strange thing. The particle passes through this slit and also passes through this slit, and not only that, but this particle interferes with itself, and the passage from here reinforces together with the passage from here the middle lobe. As if it were some kind of wave spread out in space, and it’s a particle. So what does that mean? So the accepted interpretation in quantum theory says that the particle actually passed through this slit and also through this slit. Not that I don’t know—it passed through one of them and I just don’t know which one—no, it passed through both. Like the famous example of Schrödinger’s cat: they put some capsule there with poison and an electrical circuit that is responsible for opening this capsule or not, say through beta radiation or whatever it may be, which activates an electrical circuit that opens the capsule. Now beta radiation is a quantum process, and therefore there can be a state in which we are in a superposition of either a photon being emitted in beta radiation or not being emitted. Now if it was emitted, then it opened the poison and the cat died, because the poison capsule killed the cat. If it wasn’t opened, then the cat is alive; nothing killed it. But if it’s in a state in which it both opened and didn’t open, then the cat is both alive and dead. Now that’s a little strange. About beta radiation you can say whatever you want—no one has ever seen it. But a cat that is both alive and dead—that sounds a little strange. More than a little strange, if not to say contradictory. Yes? How can it be that the cat—either if it’s alive then it’s not dead, if it’s dead then it’s not alive. How? How can it be that the cat is both alive and dead? Yes, these are the wonders of quantum theory; this is Schrödinger’s cat. What does this actually mean? It means that in quantum theory this is the only place we know of in the scientific world, in scientific theories, where there is an ontic doubt, not an epistemic one. In reality itself the particle passed through this slit and also through this slit. Not that it passed through one slit and I just don’t know through which one of the two slits it passed. That’s epistemic doubt. That exists in classical physics too. In classical physics too it could be that I don’t know whether it passed through this slit or through this slit. I don’t always know everything; if I didn’t look, then I don’t know. And then if they ask me, I’ll say: I estimate you’ll either see this kind of emission or this kind of emission. Probability one-half it’ll be this, probability one-half it’ll be this. And in the end we see both. Not probability one-half this and probability one-half this, but half here and half there. And something in the middle too. So basically it’s a quarter, a quarter, and a half, let’s say for the sake of the discussion. Okay? So that means the particle passed through slit A and also through slit B. That means that basically there is an ontic doubt here, not an epistemic one. Reality itself presents us with two possible answers. It’s not that there is an answer and I don’t know what it is; rather, reality itself says there are two possible answers here. Here you can already see, in a somewhat more similar way, the concept of free choice, and therefore it’s not by chance that various people try to hang free choice on quantum theory.

[Speaker C] Wait, did the Rabbi say that it passed through both simultaneously?

[Rabbi Michael Abraham] Yes, it passed through both here and there.

[Speaker C] So we know the answer—that it passed through both simultaneously. We have no doubt.

[Rabbi Michael Abraham] Yes, but it’s a particle that can pass through only one slit. A particle can’t pass through two slits.

[Speaker C] But what’s the doubt here?

[Rabbi Michael Abraham] It passed through both. I’m both in Australia and in Israel.

[Speaker C] Apparently, apparently there is a particle that can be in two places at the same time.

[Rabbi Michael Abraham] Those are words. Apparently there is a cat that can be both alive and dead. No, it can’t, because alive is not dead and dead is not alive. A particle that passed through slit A means it did not pass through B. A particle that passed through B means it did not pass through A. A particle that is in the sum of the two states is a particle that is in a contradictory state. It both passed through A and not through B, and passed through B and not through A.

[Speaker C] So why is it a doubt? It’s a contradiction.

[Rabbi Michael Abraham] Right, that’s what I’m saying—you call it not a doubt, and you’re right. In this context I call it an ontic doubt, because what we usually call a doubt is an epistemic doubt, where I don’t know what happened. Here I do know what happened. What happened is the two contradictory things.

[Speaker E] More than that: if you put a detector at one of them, a detector that doesn’t affect it, then the picture will come out differently.

[Rabbi Michael Abraham] Yes, then it will pass there.

[Speaker E] Right. Your knowledge determined the physics.

[Rabbi Michael Abraham] That’s already a slightly trickier question, because they did an experiment like that where the information was transmitted to a computer and then erased and destroyed, so that no human being ever encountered the information about which slit the particle passed through, and still there was collapse. Meaning, it behaved like a particle and not like a wave. So this legend that human knowledge determines the physics is a legend that apparently has been disproved.

[Speaker E] But the fact is that if you put a detector there, then you’ll get a picture of one.

[Rabbi Michael Abraham] Obviously. But even if I didn’t see that picture, the very presence of the detector turns the state into a different state.

[Speaker E] How the detector does that is the problem. That’s much more extreme, much more surprising—

[Rabbi Michael Abraham] —than the picture.

[Speaker E] I didn’t say—

[Rabbi Michael Abraham] —that I solved the problems of quantum theory. I’m only saying: those are the facts.

[Speaker E] That’s why Einstein had a hard time believing in quantum theory.

[Rabbi Michael Abraham] Right. And I’m certainly not smarter than Einstein; I don’t know how to solve this either. But those are the facts. Now that is exactly the point. The question asked here before really puts its finger on the right conceptual point. When I talk about ontic doubt, it’s not really a state of doubt; that’s just words. It’s not a state of doubt. It’s a state where everything is clear, everything is known, it’s a well-defined state—but it is made up of two possibilities that exclude one another, and therefore very often you’ll hear people refer to it as if it were a state of doubt. Ontic doubt and not epistemic. But in certain senses it’s true that it’s not really correct to treat such a state as a doubt. You know what? So that these things will be clearer, I’ll give a halakhic example. It turns out that in Jewish law there is an example that is really, really simple—you don’t need all the complications of quantum theory—and it is simply quantum superposition. There is no other way to relate to it. And that example is betrothal that is not fit for intercourse. What happens in betrothal that is not fit for intercourse? A topic in tractate Kiddushin on page 50.

[Speaker B] Suppose I sent an agent to betroth a woman, and the agent betrothed a certain woman and died. Okay? Now, once he died, I don’t know which of the women in the world is my wife. Is that an epistemic doubt or an ontic doubt? Epistemic. Epistemic,

[Rabbi Michael Abraham] right?

[Speaker B] There is one particular woman who is my wife; the Holy One, blessed be He, for example, knows who she is, right? I don’t know; I’m missing information, so that’s an epistemic doubt. But what happens if someone comes and, say, goes to a father,

[Rabbi Michael Abraham] and this father has two daughters, Rachel and Leah. He gives the father a perutah, or a ring if you prefer, and he says to him: one of your two daughters is betrothed to me. I don’t care which of the two; they’re both nice, I like them both, I can’t have two wives—one. So one of them, it doesn’t matter which. One of your two daughters is betrothed to me. And the father says: perfectly fine, it’s an honor for me, I’d be happy to become related to you, I agree. At no stage did either the groom or the father determine which of the two is the one who is betrothed. We determined that one of the two is betrothed. This concept, this situation, is called in the Talmud betrothal not fit for intercourse. What does that mean? Basically, a state of doubt has been created here—this is how the Talmud and the medieval authorities (Rishonim) describe it. After all, you know that only one is betrothed; I betrothed only one, there’s one perutah here, not two perutot. Okay? I betrothed one woman, but I didn’t define whether it was Rachel or Leah, and the father can betroth both of them, because they are his daughters.

[Speaker C] So how can you betroth in that state? It’s not betrothal at all. I didn’t say whom I’m betrothing. Nothing took effect on anyone.

[Rabbi Michael Abraham] Why should it take effect on someone?

[Speaker C] They don’t know on whom. It takes effect on no one, so there is no legal effect here to begin with.

[Rabbi Michael Abraham] You’re assuming something that is an assumption in the laws of betrothal; it has nothing to do with logic. And that assumption in the laws of betrothal is not correct, or at least is disputed—a dispute between Abaye and Rava. And betrothal not fit for intercourse is the kuf of Ya’al Kegam. The kuf of Ya’al Kegam is betrothal not fit for intercourse, where the Jewish law follows Abaye. And the claim is that there is one woman here who is betrothed, but it could be Rachel and it could be Leah, and I have no way of knowing who. But it’s not that I have no way of knowing who—there is no genuinely defined one here. Even the Holy One, blessed be He, doesn’t know who. It’s not that there is information in reality and it’s just missing for me; I don’t know whether it’s Rachel or Leah.

[Speaker C] So what’s the logic to begin with? I don’t understand the logic of saying from the outset that—

[Rabbi Michael Abraham] Wait, wait. If I had sent an agent to betroth one of them, and he betrothed one of them and died, then here there is one defined woman who is betrothed to me, and the Holy One, blessed be He, knows who she is; I don’t know—epistemic doubt. But here, in the situation I described, no particular woman was defined as betrothed. I defined that one of these two is my wife, the father agreed, there’s no problem at all—one of the two is my wife.

[Speaker C] But what do you mean, no problem at all? There was no legal effect on anyone.

[Rabbi Michael Abraham] One second, one second, I’ll answer. One of the two is my wife. Now, we didn’t define which one of the two, so that means we are in a state of quantum superposition. Literally—that is the state in the Talmud. This isn’t Torah-and-science sermonizing. It’s a state of quantum superposition. The personal-status state right now—the one registered in the rabbinate as my wife—is a superposition between Rachel and Leah. Now, what—

[Speaker C] Wait, wait, let me finish.

[Rabbi Michael Abraham] Now, the problem that arises here is that if Rachel is my wife, then Leah is my wife’s sister. My wife’s sister is one of the forbidden relations, so I am forbidden to have relations with Leah. If Leah is my wife, then Rachel is my wife’s sister, and I am forbidden to have relations with Rachel. That means that because of this doubt—whether it’s Rachel or Leah—I am forbidden to have relations with either of them. Because it could be that the other one is my wife, and then this one is my wife’s sister. So in fact I will not be able to realize these betrothals. And therefore Abaye and Rava disagree on the question whether these betrothals are valid or not. But notice: neither of them thinks like you. Both claim that in principle these betrothals are valid. One of the two is betrothed to me without defining who. One of the two. You ask: who is my wife? One of Rachel or Leah. Not epistemically—not that I don’t know. No, in reality itself. One of Rachel or Leah is betrothed to me. But now a halakhic problem is created. The halakhic problem is that this is betrothal that cannot be realized—realized through intercourse. Rava argues that such betrothal is not betrothal, because Jewish law is not prepared to allow betrothal that is not fit for intercourse. So therefore he says: I have no logical problem with this definition, that it is betrothal of one of the two; I have a halakhic problem with it, because in the end it comes out as betrothal not fit for intercourse, and therefore he says: fine, then there’s no choice, we have to say that there is no betrothal here. Not because of the logical problem. The logical problem he accepts completely. Because of the halakhic problem. Abaye argues there is no halakhic problem. True, you can’t have relations with either of them, but one of them is betrothed to you. Each of them is betrothed to you. So on the logical level, they both agree that a situation of ontic doubt is possible: that one woman out of the two is betrothed to me. And not that there is one real one and I don’t know who it is. No. It is one woman out of the two, so it could be either one of them. In another formulation, I would put it like this: basically, each of them is betrothed to me by a tenuous betrothal. Yes—not full betrothal, because only one woman is betrothed; I gave only one betrothal perutah. You can’t say that both are my wives. Incidentally, I also cannot be married to two sisters. Everyone agrees on that. You can’t be married to two sisters. Betrothal does not take effect with one’s wife’s sister. So therefore it’s clear that there cannot be full betrothal here to both women. What Abaye argues—and Rava also agrees on the logical level were it not for the problem that this is not fit for intercourse—what Abaye argues, and this is also the Jewish law, yes, that this is indeed betrothal—Abaye is basically saying: correct, there is one woman who is betrothed to me, but that woman is not a defined woman. It is one of the two. And therefore, for each of them a state is created that is as if it were a doubt. It’s not a doubt; there is no doubt here at all. But it is like a doubt. From this point on I’ll call it ambiguity, as distinct from doubt. Doubt is epistemic doubt, where I lack information. Reality is defined; I just don’t know the full information about reality. Ontic doubt—from now on I won’t call it doubt, I’ll call it ambiguity. What does that mean? Reality itself is ambiguous. Not that I don’t see it clearly or don’t have all the information, but that in reality itself there is ambiguity. The mathematical tool that deals with doubts is probability and statistics. Now we’re getting to the subject of the series: doubts and probability. The tool that deals with ambiguous states is what’s called fuzzy logic. Ambiguous logic. Okay? And in principle that is not statistics. Statistics is an example of fuzzy logic—it doesn’t matter in the mathematical structure—but what is called fuzzy logic in this context is not statistics; it’s something else. Because statistics examines probabilities among different events that exclude one another—whether this event happened or that event happened. So I have statistics like throwing a die or flipping a coin or something like that. So that essentially deals with lack of information, with partial information. Statistics deals with partial information.

[Speaker F] If I want to solve the doubt and I go to the husband and say, listen, this can’t go on like this, choose—can I thereby solve the doubt?

[Rabbi Michael Abraham] That’s the next column, and I’m not going into it because it doesn’t concern us. The next column on my website—this column, what number is it, I already don’t remember—three-two-two. Three-two-two, three-two-three—those are the two columns about what I’ve talked about until now. In three-two-four I deal with the problem of collapse in Jewish law, quantum collapse in Jewish law. There is superposition in Jewish law too. The question is whether there is also collapse in Jewish law. Collapse means that I can put a detector there and turn this wave into a particle. Can I turn this state of betrothal of one out of two women into a state where I choose one of them and it collapses into a state where Rachel will be my wife? For example, if the father and I later agree: okay, let’s decide that it will be Rachel. Afterward. Meaning, I already performed the betrothal. The betrothal took effect in the ambiguous way I described before. The question is whether we have the power now to decide: okay, let’s collapse the wave function and determine that Rachel will be my wife. This is a dispute among medieval authorities (Rishonim) and later authorities (Acharonim). It’s very interesting, not very well known, so anyone who wants can look at that column, three-two-four. But that really pertains only to the interpretation of quantum theory. What interests me is only the state of ambiguity; collapse and all that is an anecdote in this context. Okay, I’ll stop here because I’ve defined the two concepts, and we’ll continue from here next time.

[Speaker C] Is there a halakhic example of a state of ambiguity?

[Rabbi Michael Abraham] There are several such examples, yes. For example, if I consecrated one coin out of several coins in my pocket. I consecrated ten cents. I have several ten-cent coins in my pocket and I consecrated one of them, without determining which one, I didn’t point to any particular one—one of the coins in my pocket is consecrated property. Or payment received for a dog, it doesn’t matter. There are several examples in the Talmud that are ontic doubt. Now, you can look at my columns there where I bring them—Rabbi Shimon Shkop talks about this. There are examples of this in Jewish law. And that’s what is beautiful here: the halakhic example is very simple to understand in principle; we understand what is happening there. All the complications in quantum theory somehow do not trouble us when we are here, because here we are talking about a legal status, not a physical reality. Regarding legal status, we have no principled problem accepting a legal definition that one of two women is defined as my wife. But after all, the cat being alive or dead—that is a physical state; either it is alive or it is dead. So what does it mean that the cat is both alive and dead? But to say that both Rachel is my wife and Leah is my wife, even though they are two sisters and so it cannot be that both are my wives—a person cannot be married to two sisters. Rather, both Rachel is my wife and Leah is not, and Leah is my wife and Rachel is not. That is a sum of two states, each one of which is only a single-particle state, like one woman. The particle both passed through slit A but not B, because it is a particle, and the particle passed through B but not A. It’s not correct to say that what’s involved is that the particle passed through both A and B; that’s the crude, balebatish description. The more correct description in terms of quantum theory is: the particle is both in a state in which it passed through A and not B, and in a state in which it passed through B and not A. Okay? To say it passed through both A and B is to say it is a wave, but that’s not correct. That is not the meaning of a quantum wave; that’s in popular science books, but it’s not really right. It’s exactly like the betrothal of the woman: both Rachel is betrothed to me, and then according to Jewish law Leah cannot be my wife because she is my wife’s sister, and Leah is my wife, but then Rachel cannot be my wife. So it’s both this and that, but it’s a superposition between two states, in each of which only one of them is my wife. The other is my wife’s sister; she cannot also be my wife. Okay? Good—if there are comments or questions, then fine, we’ll stop here. Thank you very much. Thank you, Sabbath peace.