An interview with

H: So that’s the Center for Rationality. I know this doesn’t belong, but I’ll ask it here. You are a deeply religious man. How does it fit in with a rational view of the world? How do you fit together science and religion?

A: As you say, it really doesn’t belong here, but I’ll respond anyway. Before responding directly, let me say that the scientific view of the world is really just in our minds. When you look at it carefully, it is not something that is out there in the real world. For example, take the statement “the earth is round.” It sounds like a very simple statement that is either true or false. Either the earth is round or it isn’t; maybe it is square, or elliptical, or whatever. But when you come to think of it, it is a very complex statement. What does roundness mean? Roundness means that there is a point—the “center” of the earth—such that any point on the surface of the earth is at the same distance from that center as any other point on the surface of the earth. Now that already sounds a little complex. But the complexity only begins there. What exactly do we mean by equal distance? For that you need the concept of a distance between two points. The concept of distance between two points is something that is fairly complex even if we are talking about a ball that we can hold in our hands; it involves taking a ruler and measuring the distance between two points. But when we are talking about the earth, it is even more complex, because there is no way that we are going to measure the distance between the center of the earth and the surface of the earth with a ruler. One problem is that we can’t get to the center. Even if we could find it we wouldn’t be able to get there. We certainly wouldn’t be able to find a ruler that is big enough. So we have to use some kind of complex theory in order to give that a practical meaning. Even when we have four points and we say the distance from A to B is the same as the distance from C to D, that is fairly complex already. Maybe the ruler changes. We are using a whole big theory, a whole big collection of ideas, in order to give meaning to this very, very simple statement that the earth is round.

Don’t get me wrong. We all agree that the earth is round. What I am saying is that the roundness of the earth is a concept that is in our minds. It’s a product of a very complex set of ideas, and ideas are in people’s minds. So the way I think of science, and even of fairly simple things, is as being in our minds; all the more so for things like gravitation, the energy that is emitted by a star, or even the concept of a “species.” Yes, we are both members of the species homo sapiens. What does that mean? Obviously we are different. My beard is much longer than yours. What exactly does species mean? What exactly does it even mean to say “Bob Aumann” is sitting here? Is it the same Bob Aumann as five minutes ago? These are very complex ideas. Identity, all those things that we think of trivially on a day-to-day basis, are really complex ideas that are in our minds; they are not really out there. Science is built to satisfy certain needs in our minds. It describes us. It does have a relationship with the real world, but this relationship is very, very complex.

Having said that, I’ll get to your question. Religion is very different from science. The main part of religion is not about the way that we model the real world. I am purposely using the word “model.” Religion is an experience—mainly an emotional and aesthetic one. It is not about whether the earth is 5,765 years old. When you play the piano, when you climb a mountain, does this contradict your scientific endeavors? Obviously not. The two things are almost—though not quite—orthogonal. Hiking, skiing, dancing, bringing up your children—you do all kinds of things that are almost orthogonal to your scientific endeavor. That’s the case with religion also. It doesn’t contradict; it is orthogonal. Belief is an important part of religion, certainly; but in science we have certain ways of thinking about the world, and in religion we have different ways of thinking about the world. Those two things coexist side by side without conflict.

H: A world populated by rational players—is it consistent with the religious view?

A: Yes. Religion places a lot of emphasis on coliving with your fellow man. A large part of religion is, be nice to other people. We can understand this in the religious context for what it is and we can understand it scientifically in the sense of repeated games that we discussed before, and we can understand it from the evolutionary viewpoint. These are different ways of understanding the phenomenon; there is no contradiction there. Fully rational players could be deeply religious; religion reflects other drives.

H: This applies to person-to-person interaction. But isn’t there, in a sense, an extra player, which would be G-d or something that you cannot understand by rational means, an extra non-rationally driven player?

A: My response is that each player has to see to his own actions. In discussing the laws, the rules by which we live, the Talmud sometimes says that a certain action is not punishable by mortal courts but is punished by Heaven, and then discusses such punishments in detail. Occasionally in such a discussion somebody will say, well, we can only determine what the reaction of human courts will be to this or that action. We cannot dictate to Heaven how to react, and therefore it’s useless for us to discuss it. That cuts off the discussion. As a religious person I must ask myself how I will act. I cannot discuss the rationality or irrationality of G-d.

H: The point is not the rationality or irrationality of that player, of G-d, but how that player affects what other players do and in what ways rational players can take this into account. Let me make it very simplistic. As you said, you don’t know what Heaven will do, so how can I make rational decisions if I don’t know that?

A: We don’t know what Heaven will do, but we do have rules of conduct. We have the Pentateuch, the Torah, the Talmud.

H: I am talking more on the philosophical level, rather than on a practical level. The point is that that player is not reducible to standard mortal arguments or understanding. Because if he were he would not be a special entity, which G-d is. However, he is part of the world. Not only is he part of the world, he is an important part of the religious world. He is not just a side player. He is the main player. Not only is he the main player, he is a player who by definition cannot be reduced to rational analysis.

A: I wouldn’t say that He is irrational. By the way, it is interesting that this should come up just today, because there is a passage in the Torah reading of yesterday that relates to this. “This commandment that I command you today is not far away from you. It is not in Heaven so that one would have to say, ‘Who will go up to Heaven and will take it from there and tell us about it?’” (Deuteronomy 30, 11–12). These verses were interpreted in the Talmud as saying that in the last analysis, commands in the Torah, the religious commandments, the whole of Scripture must be interpreted by human beings, by the sages and wise men in each generation. So the Torah must be given practical meaning by human beings.

The Talmud relates a story of a disagreement between one of the sages, Rabbi Eliezer ben Horkanos, and all the other sages. Rabbi Eliezer had one opinion and all the others had a different opinion. Rabbi Eliezer said, if I am right then let the water in the aqueduct flow upwards. Sure enough, there was a miracle, and the water started flowing uphill. So the other sages said, we are sorry, the law is not determined by the way the water flows in an aqueduct. It is determined by majority opinion. He asked for several other miracles and they all happened—Heaven was on his side. Nevertheless, his opinion was rejected. Each time the majority rejected it and said this is irrelevant. In the end he said, if I am right let a voice come from Heaven and say so. And sure enough, a voice came from Heaven and said, why do you argue with Rabbi Eliezer, whatever he says is always right. This was again rejected by the majority, who quoted the verse I just cited, “It is not in Heaven.” The Torah was given to us by Heaven, and now it is our prerogative to interpret it. The story goes on to say that Elijah (the prophet who never died and keeps going back and forth between Heaven and earth) was asked by one of the sages who met him, were you in Heaven when that happened? He said, yes, I was there. The sage said, how did G-d react to his opinion being rejected by the earthly sages? So Elijah said, G-d smiled and said, “My children have vanquished me.”

This is an example of what is behind the figure of G-d—call it a model, a way of thinking, a way of living. It is similar, broadly speaking, to the earth being round. G-d is a way of thinking of our lives; translated into practical terms, it tells us how to live as human beings.

H: This is very interesting. Let me try to summarize. On the one hand there is an emotional and aesthetic experience, to which I can very clearly relate, like going to a concert or seeing something beautiful. On the other hand, religion dictates certain rules of behavior. These rules, first of all, are not well defined. They are interpreted by human beings. Second, these rules may be justified in a rational way. Like in your work with Michael Maschler [46], where you gave a game-theoretic interpretation of a passage from the Talmud that nobody could understand, and suddenly everything became crystal clear. So you are saying that there are rules, which are good rules. And they are good not just because G-d gave them to us. We may not understand the reasons, but if we go deep enough and start analyzing, we may find good reasons for them. Moreover, if people are following these rules it leads perhaps to a better society—a Pareto improvement. Is that correct?

A: Well, it is your way of putting it. Let me enlarge on it. The observance of the Sabbath is extremely beautiful, and is impossible without being religious. It is not even a question of improving society—it is about improving one’s own quality of life. For example, let’s say I’m taking a trip a couple of hours after the Sabbath. Any other person would spend the day packing, going to the office, making final arrangements, final phone calls, this and that. For me it’s out of the question. I do it on Friday. The Sabbath is there. The world stops.

H: That’s a good example. In fact my wife has said many times, after yet another guest suddenly dropped in on us on Saturday, or we had to go and do something or other: “I wish we would become religious and have a really quiet Saturday once in a while.” So I can definitely understand the advantages of having a nice, quiet day of rest.

A: The day before the Sabbath, Friday, is a very hectic day for the person in charge of the house, who has to prepare for the Sabbath. On Friday in Israel, like on Saturday in most of the western world, many offices are closed. It is a semi-day-of-rest. But for religious people, especially for the houseperson, it is very hectic. We have a seminar series at the Center for Rationality called “Rationality on Friday”; my wife used to say that she could understand rationality on any other day, but not on Friday.

So, we have this one day in the week when nothing can come in the way and we are shut off from the world. We don’t answer the phone, we don’t operate electricity, we don’t drive cars.

H: It is a self-committing device, if you translate it into rational terms.

A: Exactly, it’s a self-committing device.

Here is another example. There was a period fifteen, twenty years ago when stealing software was considered okay by many people, including many academics. There was an item of software that I needed, and I was wondering whether to “steal” it—make a copy of which the developers of the software disapprove. Then I said to myself, why do you have to wonder about this? You are a religious person. Go to your rabbi and ask him. I don’t have to worry about these questions because I have a religion that tells me what to do. So I went to my rabbi—a holocaust survivor, a very renowned, pious person. I figured he won’t even know what software is—I’ll have to explain it to him. Maybe there is a Talmudic rule about this kind of intellectual property not really being property. Whatever he’ll say, I’ll do. I went to him. He said, ask my son-in-law. So I said, no, I am asking you. He said, okay, come back in a few days. I’ll make a long story short. I went back again and again. He didn’t want to give me an answer. Finally I insisted and he said, “Okay, if you really want to know, it’s absolutely forbidden to do this, absolutely forbidden.” So I ordered the software.

In short, you can be a moral person, but morals are often equivocal. In the eighties, copying software was considered moral by many people. The point I am making is that religion—at least my religion—is a sort of force, a way of making a commitment to conduct yourself in a certain way, which is good for the individual and good for society.

H: But then, in a world where everybody follows these rules, there is perhaps no reason for game theory. Of course, there is a problem in the details; the rules of conduct may not be enough to tell you exactly what to do in every situation. But in principle, in a world populated by religious people, do we need game theory?

A: Certainly. The rules cover only the moral or ethical issues. There is a lot of room within these rules for strategic behavior. For example, the rules tell you that if you made an offer and it was accepted, then you can’t renege. But they don’t tell you how much to offer. The rules tell you that you must bargain in good faith, but they don’t tell you whether to be tough, or compromising, or whatever. The rules tell you, “You may not steal software”; but they don’t tell you how much to pay for the software, when to buy it and when not. The rules tell you to give a lot to charity, but not how much. There was a study made in the United States of income tax deductions to charity. It turned out that orthodox Jews were among the largest contributors to charities. It’s a religious command.

Unfortunately it has been my lot to spend more time in hospitals than I would have wanted. I have witnessed some very beautiful things. People coming to hospital wards and saying, look, we have private ambulances. We can take people from this hospital to wherever you want to go, from Metulla to Eilat (the northern and southern extremities of Israel), for nothing. We’ll take anybody, religious, irreligious, Jews, Arabs, anybody. These were people who obviously were religious. They were going around with a beard and sidelocks. You have people who come around on Friday afternoon to make kiddush for the sick, and people who come around at any time of the week playing the violin and things like that.

The religious community, by the way, is very close. This matter of khessed, of helping your fellow man, is very strong in religious communities; it is a commandment, like eating kosher and keeping the Sabbath.

H: Returning to the rules and their interpretation: do you mean that you would not go to the rabbi to ask him, say, whether to enter into a certain partnership, or how to vote in an election?

A: Well, I would not, and many others like me would not. But others—for example, “Khassidim”—might well consult their rabbi on such matters. In Khassidic circles, the rabbi is often much more than a scholar and legal and spiritual authority. He is a fountain of advice on all kinds of important decisions—medical, business, family, whatever. And often he gives very good advice! How come? Is he smarter than others? Yes, he often is. But that’s not the important reason. The important reason is that everybody comes to him, so he gets a whole lot of inside information. We have a very interesting strategic equilibrium there—it’s optimal for everyone to go to him, given that everybody goes to him! Of course, for that it is important that he be honest and straightforward, and that’s already dictated by the moral rules. But it’s also part of the equilibrium, because the whole thing would fall apart if he weren’t.

There is, incidentally, a phenomenon like this also among the “Mitnagdim,” like me. There is a person in Israel called Rabbi Firer, who is absolutely the top source of medical information in the whole country, possibly in the whole world. And he is not a physician. Anybody who has an unusual or serious medical problem can go to him, or phone him. You make a phone appointment for, say, 1:17 a.m., you describe your problem, and he tells you where to go for treatment. Often the whole thing takes no more than a minute. Sometimes, in complicated cases, it takes more; he will not only direct you to a treatment center in Arizona, he’ll arrange transportation when necessary, make the introductions, etc., etc. The whole point is that he is not a physician, so he has no special interests, no axe to grind. How it works is that he, like the Khassidic rabbi, gets information from everybody, patients and doctors alike, and he is also unusually brilliant. And he is deeply religious, which, again, is what keeps him honest. I have made use of him more often than I would have liked.

Up to now we have been discussing the normative side of game theory—advising individuals how to act—but there are also other sides. One is “public normative.” The religion will not tell you how to conduct elections, or when to cut the discount rate, or how to form a government. It will not tell you how to build a distributed computer, or how to run a spectrum auction, or how to assign interns to hospitals.

Still another side is the “descriptive.” Religion will not explain how evolution formed various species, or why competition works.

But I must immediately correct myself: the Talmud does in fact discuss both evolution and competition. Evolution is discussed in the tractate Shabbat on page 31a. The sage Hillel was asked why the eyes of certain African tribesmen are smaller than usual, and why the feet of other African tribesmen are broader than usual. Hillel’s answers were adaptive: the eyes are smaller because these tribesmen live in a windy, sandy region, and the smallness of the eyes enables them better to keep the sand out; and the feet are broader because that tribe lives in a swampy region, and the broad feet enable easier navigation of the swamps.

Competition is also discussed in the Talmud. In the tractate Baba Bathra 89a, the Talmud says that the authorities must appoint inspectors to check the accuracy of the weights and measures used by marketplace vendors, but not to oversee prices. The twelfth-century commentator Samuel ben Meier (Rashbam) explains the reason: if a vendor overcharges, another vendor who needs the money will undercut him, all the customers will go to him, and the original vendor will have to match the lower price. The invisible hand—600 years before Adam Smith!

Other game-theoretic and economic principles are also discussed in the Talmud. The nucleolus makes an implicit appearance in the tractate Kethuboth 93a [46]; risk aversion shows up in Makkoth 3a [80]; moral hazard, in Kethuboth 15a, and the list can be made much longer.

But of course, all these discussions are only the barest of hints. We still need the game theory to understand these matters. The Talmud speaks about adaptation, but one can hardly say that it anticipated the theory of evolution. The Talmud discusses competition, but we can hardly say that it anticipated the formulation of the equivalence theorem, to say nothing of its proof.

Besides, one needs game theory to explain the ethical and moral rules themselves. Why not steal software? Why have accurate weights and measures? Why love one’s neighbor as oneself? How did it come about, what function does it serve, what keeps it together? All these are game-theoretic questions.

Finally, let’s not forget that the world is very far from being—to use your phrase—populated by religious people only.

In short, the Bible and the Talmud are fascinating documents, and they cover a lot of ground, but there still is a lot of room for game theory­—and for all of science.

H: So, to summarize this point: game theory definitely has a place in a religious world. In the “micro,” the rules of conduct are principles that cover only certain issues, and there is “freedom of decision.” In the “macro,” the structures that arise, and the rules of conduct themselves, are subject to game-theoretic analysis: how and why did they come about?

Is your view a common view of religious people?

A: Maybe not. One doesn’t discuss this very much in religious circles. When I was young, there were many attempts by religious people to “reconcile” science and religion. For example, each of the six days of creation can be viewed as representing a different geological era. There was—and perhaps still is—a view that science contradicts religion, that one has to reconcile them. It is apologetic, and I don’t buy it.

H: Take for example the six days of creation; whether or not this is how it happened is practically irrelevant to one’s decisions and way of conduct. It’s on a different level.

A: It is a different view of the world, a different way of looking at the world. That’s why I prefaced my answer to your question with the story about the roundness of the world being one way of viewing the world. An evolutionary geological perspective is one way of viewing the world. A different way is with the six days of creation. Truth is in our minds. If we are sufficiently broad-minded, then we can simultaneously entertain different ideas of truth, different models, different views of the world.

H: I think a scientist will have no problem with that. Would a religious person have problems with what you just said?

A: Different religious people have different viewpoints. Some of them might have problems with it. By the way, I’m not so sure that no scientist would have a problem with it. Some scientists are very doctrinaire.

H: I was just reminded of Newcomb’s paradox, with its “omniscient being.” We both share the view that it doesn’t make much sense. On the other hand, perhaps it does make sense in a religious world.

A: No, no. It’s a little similar to this question of the omnipotence of G d. If G-d is omnipotent, can he create an immovable object? Atheists will come up with a question like that, saying, here, I’ve disproved the whole idea of religion.

By the way, it’s not a Jewish view that G-d is omnipotent. But that’s not the point; the point is that the question is simply nonsense.

Altogether, the Jewish tradition is not very strong on theology, on what it is that G-d can or cannot do. But there is a very strong tradition of human free will in Judaism. There is definitely one thing that G-d cannot do, namely, influence a person’s free will, his decision-making capacity. So there is a lack of omnipotence at least in that aspect of the Jewish tradition.

H: Rational people can very well exist in this religious world. You have reconciled that very nicely. That was very interesting.

A: I haven’t reconciled. I tried not to reconcile, but to say, these are different things.

H: Reconciled in the sense that those things can coexist.

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Let’s move now to your personal biography.