Faith – Lesson 11

Table of Contents

• A dead end between philosophy and the sciences
• Intuition as faith / belief and as a foundation of knowledge
• Ways of arriving at faith and Kant’s classification
• Simple faith and the danger of pragmatism
• The argument from morality and tradition
• Different concepts of God according to different arguments, and Occam’s razor
• Moving from the philosophical God to the religious God
• Pascal’s wager and its formulation
• Dawkins’s critique and the response within this framework
• Faith / belief as a spectrum and partial justification for pragmatics
• The statistical critique of Pascal: expected value versus frequency
• Applying the critique to Pascal and buying a “ticket” of commandments
• Examples of probabilistic intuitions, miracles, and the “law of small numbers”
• Conclusion: removing the wager and keeping the six ways

Summary

General Overview

The text presents a dead end on the way to faith in God between a philosophical-logical toolbox, which seems to beg the question, and a scientific-observational toolbox, which cannot arrive at God because there is no way to observe Him or to put the claim to a falsifiability test. The proposed solution is a third path: non-sensory observation called intuition, defined as a cognitive faculty that is synonymous with faith / belief and that also serves science and every system of knowledge. From within this framework, the text presents different ways of arriving at faith, identifies the dangers of pragmatism, and gives a broad presentation of Pascal’s wager together with the critique that its central failure is statistical, and that relying on expected value is not a good decision criterion in cases of tiny probabilities and infinite gains.

A dead end between philosophy and the sciences

The philosophical-logical toolbox appears futile because faith in God is a claim about the world, not a statement about a feeling, and claims about the world are not acquired merely because a person is “built” religiously. The scientific-observational toolbox cannot yield God because there is no observational access to Him, and the claim that God exists is not a scientific claim and cannot be falsified. The failure of both toolboxes sends one back to fundamentalism or skepticism within the framework of the “three paths of maturation.”

Intuition as faith / belief and as a foundation of knowledge

The text argues that there is a third way to gather information about the world through non-sensory observation called intuition, which is direct perception not mediated by proofs and not mediated by the senses. Human intuition is described as synonymous with faith / belief and as a cognitive faculty underlying every system of knowledge, including science. Faith in God is presented as not exceptional compared to other theoretical domains, because all of them rely on the same type of basic tool.

Ways of arriving at faith and Kant’s classification

The text presents three ways according to Kant’s classification: the ontological proof from conceptual analysis, the cosmological proof according to which if something exists there must be someone who created it, and the physico-theological proof based on the complexity of the world, the coordination among its parts, and their orientation toward a purpose. Kant classifies things this way because a proof begins either from concepts alone, or from existence itself without character, or from the character of the things that exist in the world. The text adds a path of direct intuition, in which a person claims that faith in God itself is his intuition, and he does not need other premises from which to derive God’s existence.

Simple faith and the danger of pragmatism

The text identifies direct intuition with what in Jewish thought and Christian thought is called simple faith, in which a person feels that there is a God, and therefore there is a God, without philosophy and without sophisticated arguments. The text raises a warning flag about the danger of pragmatism if “feeling” means an emotion that is morally or psychologically useful to a person but says nothing about reality. The path is legitimized when intuition is understood as a cognitive tool akin to seeing a table, even if a person sometimes calls it a “feeling” because he lacks more precise concepts.

The argument from morality and tradition

The text includes an argument from morality in the form “if there is no God, there is no morality,” and expands it into theological arguments in quotation marks, while linking it to the danger of pragmatism because it may “create” God in order to provide a foundation for morality. The text also includes tradition as a path to faith, such as the revelation at Mount Sinai or a religious tradition in which someone encountered God and passes on a reliable chain regarding that encounter. The text notes that different people justify faith through different paths from this list, and it corrects the count from seven to six before presenting a seventh way.

Different concepts of God according to different arguments, and Occam’s razor

The text argues that each argument points to a different object, and therefore one has to define which entity is being proved: the ontological argument proves “the perfect being,” the cosmological argument proves the creator of the world, the physico-theological argument proves the “engineer” who designs, the moral argument proves the one who gives validity to the laws of morality, and the argument from tradition proves the one revealed at Sinai or the creator of the world, depending on the religion. The text emphasizes that this does not mean there are six gods, and it may be that this is the same entity viewed from different aspects. The text adds Occam’s razor as a preference for fewer entities, and suggests that if one accepts several proofs together they may strengthen one another, even if a person accepts only some of them and still reaches the conclusion that there is a God.

Moving from the philosophical God to the religious God

The text states that the next step will be to lay out “route by route” how one arrives at God, and then ultimately to connect the philosophical God to the religious God and show how one gets from here to religious faith and religious commitment. The text presents Pascal’s wager as a seventh way that must be discussed in order to complete the picture, even though it is claimed to be mistaken.

Pascal’s wager and its formulation

The text presents Blaise Pascal as a French philosopher, mathematician, statistician, physicist, and theologian from the seventeenth century, and describes a powerful religious experience he had at the age of thirty-one. Pascal proposes a statistical argument that makes proofs unnecessary: it is better to believe, because if there is a God one gains eternal happiness, and if there is no God then “it’s not so terrible,” whereas non-belief in a world with God leads to eternal punishment, and non-belief in a world without God “doesn’t matter.” The text formulates this as an expected-gain calculation and compares the structure to a valid dilemma argument in logic, in which both horns of the dilemma lead to the same conclusion.

Dawkins’s critique and the response within this framework

The text quotes Dawkins as saying that Pascal’s wager is pragmatic, and belief is not a voluntary act that one can decide on as a matter of policy; at most one can pretend to believe, and an omniscient God would detect the pretense. The text presents an additional claim about “there is no authority over matters of fact,” and distinguishes between authority that obligates action and a demand to believe a fact when a person is not convinced. The text discusses whether belief can be bypassed through observance of commandments alone, and expresses the position that there is no value in observing commandments without faith, including an example of putting on tefillin for a person who does not believe, and the claim that cultural-national observance in the style of Ahad Ha’am is not “observing the Sabbath” in the religious sense.

Faith / belief as a spectrum and partial justification for pragmatics

The text rejects a binary state of belief or heresy and presents a spectrum of degrees, including a seven-point scale that Dawkins himself proposes, with his own position at level two from the edge. The text argues that there is no absolute certainty about anything, and therefore not about faith in God either, and people in any case make decisions under conditions of uncertainty. The text allows that in a state of genuine indecision, considerations of expected gain may be relevant, and that a person can choose to “go with belief” on the chance that there is a God, while discussing the question of whether such observance of commandments would count, together with a remark about distinguishing between positive commandments and prohibitions.

The statistical critique of Pascal: expected value versus frequency

The text argues that the decisive critique of Pascal is actually statistical rather than theological, because the criterion of expected value is not always a good criterion for decision-making when the average gain rests on extremely rare events. The text presents an example of a biased coin with a tiny probability of an astronomical payoff and asks how much a person would invest in the ticket, arguing that no sane person would sell his house even if the expected gain were enormous. The text presents the St. Petersburg paradox in a game of powers of two, where the expected gain is infinite but the typical gain is small, and concludes that the chance of reaching the average payoff is negligible in a single trial. The text states that expected value is relevant when dealing with frequent situations, but in pathological cases of highly skewed distributions one should not act according to expected value.

Applying the critique to Pascal and buying a “ticket” of commandments

The text applies this to an atheist who estimates the probability of God at one in ten thousand, and argues that from his perspective there is no reason to “buy a ticket,” meaning to pay the price of observing commandments, if the chance of infinite gain is tiny. The text compares this to taking everyday risks such as going out onto the road, and explains that people are not willing to subordinate their lives to a small risk, and that this is rational behavior. The text brings in the utility function and emphasizes that a significant price depends on the person, and therefore even if expected value “instructs” one to invest a large sum, in practice people act according to the weight of the cost and the chance in terms of their own utility. The text concludes that Pascal’s mistake lies in turning expected value into a universal decision criterion instead of recognizing its limitations.

Examples of probabilistic intuitions, miracles, and the “law of small numbers”

The text tells a personal story about a nighttime accident near Gedera, in which a neighbor from Yeruham with a large vehicle appeared at exactly the right time and drove the family, and presents the temptation to see this as an open miracle. The text argues that one cannot know whether this departs from statistics without knowing the sample space, and that one rare case is supposed to happen to someone when there are enough trials. The text gives an example from a suspense book in which 10,000 letters are sent in order to “predict” the correct number for a few people, and presents this as a principle according to which only the successful cases get publicized. The text calls this the “law of small numbers” and warns against using probability when one does not know the broader context, while raising an internal debate over whether, if one attributes involvement in events to God, one should also attribute both the accident and the rescue to Him.

Conclusion: removing the wager and keeping the six ways

The text declares that the goal of the session is to remove Pascal’s wager from the map of possible ways to arrive at faith and to remain with the six ways listed earlier. The text ends with questions from the audience about the difference between monetary profit and infinite spiritual gain, and with the response that this is a matter of a personal utility function that does not statistically obligate every person, and it concludes with a farewell of Shabbat Shalom.

Okay, let’s see where we were last time. I talked about different paths—in other words, I talked about the fact that there’s some kind of broken trough on the road to belief in God. On the one hand, there’s the philosophical-logical toolbox, and the alternative is the scientific-observational toolbox. The philosophical-logical toolbox seems futile, because when I say I believe in God, that’s some kind of claim about the world—I prefaced this with various premises—and it’s not a statement about my feelings. Claims about the world, seemingly, can’t be made just because that’s what I think or that’s how I’m built. The fact that I’m built in a religious way doesn’t mean there is a God in the world. For that, seemingly, you need some kind of indication that results from observation or something like that. So philosophy and logic—yes, that’s begging the question and the emptiness of the analytic and of logic—that’s what we discussed on the one hand. On the other hand, the scientific-observational toolbox can’t give us God, because there’s no way to observe Him, not even indirectly. We have no access through scientific tools to reach God. The claim that God exists is not a scientific claim; it can’t be subjected to falsification. So it comes out that both possible toolboxes fail to do the job, which sends us back to fundamentalism or skepticism, if you remember the three paths of maturation that I talked about. And then I said that the only way out of this—which is really also the only way to define philosophy in general, because what I just said is, in a certain sense, a critique of philosophy altogether—is to claim that there is also a third way to accumulate information about the world: through non-sensory observation, what I called intuition. That is basically some ability we have to grasp something in the world directly—not through proofs and not through our senses, but to understand directly the general law, for example in the laws of nature and the like. And then my conclusion was that human intuition, which serves us in many areas, is, you could say, a synonym for faith. Faith is some kind of cognitive faculty. It’s not only a state in which I believe in God; it’s the result of using tools that I call faith. Those tools are basically intuition. And in that sense it isn’t necessarily only on the theological plane; science too is built on these tools. Every system of knowledge about the world is fundamentally built on these tools, and therefore belief in God is not unusual in that sense compared to any other intellectual or scientific field. Then I went on and said that I want to see how I use this system of tools—intuition—and arrive at belief in God. So I think we can speak of seven ways to do that. There are three ways in Kant’s classification, which we’ll get to in a moment. One of them is the way of conceptual analysis, what he calls the ontological proof. The second is the cosmological proof: if something exists, there must be someone or something that created it—the cosmological proof. And the physico-theological proof is a proof based on the properties of the existing thing—its complexity, the coordination between its parts, its directedness toward a goal, its purposiveness—and that is the basis of the physico-theological claim. Kant classifies it into these three types because he argues that this basically covers all possible proofs, since a proof has to start somewhere. Either it starts from conceptual analysis, unrelated to reality—and that’s the problem with the philosophical toolbox, we’ll get back to that in a moment—or it starts from the very existence of something, without addressing the question of what kind of thing it is, but then it already touches the world, just not the character of the thing that exists in the world; that’s the cosmological proof. And the physico-theological proof is based on the character of what exists in the world, on the specific things we see in the world, from which one can derive the existence of a creator, a maker. So those are Kant’s three paths. There is also a way we can call direct intuition. I said that if at the foundation of every logical-philosophical argument there are premises, one can always ask: where do we learn those premises from, where do we draw them from? And the answer will always be: from intuition. So there’s no obstacle to a situation in which a person comes and says: you know what? Belief in God is itself my intuition. I don’t need other intuitions that will give me basic assumptions from which I derive God’s existence; I have an intuition that God exists. And this is what, in the language of Jewish thought—or actually also in Christian thought—is called simple faith. Simple faith means without philosophies and without sophisticated arguments; I feel or sense within myself that God exists, and therefore God exists. Here one has to distinguish between two… All of this is a discussion conducted within the framework I described up to this point. Earlier I talked about fundamentalism and skepticism. Now notice that the ontological proof talks about the philosophical toolbox. The… wait. Yes, direct intuition talks about my direct sense that God exists. But with that sensation there is already a danger of pragmatism. I’m raising a warning flag here: the danger of pragmatism. What does that mean? If a person says, I have a sense that God exists in the sense of an emotion—that proves nothing. It means you are built in a religious way. The question is: what does that say about the world? Does such an entity as God actually exist in the world itself? So what do your feelings have to do with that? If you say that it helps you to assume that God exists because it gives you morality or all sorts of things like that, none of that interests me. That’s pragmatism, which is not supposed to say anything about reality itself. But if you say: I have an intuition that God exists, and intuition, as I said before, is an observational tool—I simply experience God’s existence, and therefore in my opinion God really does exist—that’s like if someone asked me why I think there’s a table in front of me. My answer is not a philosophical argument; I simply see that there is a table here. Is that an emotion? No, it’s not an emotion. I see that there’s a table, and therefore there’s a table here. So that person, the person of simple faith, will say: I see that God exists, and therefore God exists. Obviously I don’t see with my eyes; I see with the eyes of the intellect, with my intuition. But as long as he understands that this is a cognitive tool and not an inner feeling, then that too is a legitimate path to belief in God. And by the way, even if he doesn’t understand that—even if he doesn’t understand it and sometimes says, I have such a feeling—in many cases he doesn’t actually mean emotion; he just doesn’t have the right conceptual framework, so he calls it emotion. But really he means intuition. Therefore a person often doesn’t understand himself, doesn’t know how to formulate himself—those are different things, either this or that—but his faith is still proper faith because it is based on intuition. So that’s the fourth path. We have Kant’s three paths, we have direct intuition—that’s the fourth path. We have the argument from morality, which Kant also raises, though not in the Critique of Pure Reason. I’ll expand that into what I call “theological” arguments, in quotation marks. That is, this is a whole pattern of a different kind of argument. If there is no God, there is no morality. Claims of that sort. Those are the fifth kind of arguments, and that too connects us to pragmatism, because when I say that if there is no God there is no morality, I am essentially inventing God so that there will be morality in my world. That’s not a direct intellectual argument. Fine, so there’s no morality—what can you do? But still, who says there is a God? Therefore here too there is a danger of pragmatism. I’ll detail all that later; right now I’m just trying to sketch the overall picture. That’s the fifth argument. The fifth—or really the sixth, I think. I talked about Kant’s three, I talked about direct intuition, the fifth is the argument from morality, and then tradition. So apparently there are six arguments, not seven. There are those who rely, say, on the revelation at Mount Sinai or some other religious tradition. Someone met God. Someone met God and passes on to me the tradition about that encounter. If I regard that tradition as a reliable chain, then that too is a way to arrive at the existence of God. All these ways are found among people. Ask people why they believe, and they’ll answer you in different ways; different people will answer you with each of these seven paths—six paths, and in a moment I’ll explain why I keep saying seven. And one last point before we really start down this path: these arguments, each one of them—I mentioned this, I’m just summarizing where we were last time—each of these arguments speaks about a different object, a different God. Every such argument has to define who the object is whose existence I am proving. The ontological proof will prove the existence of the perfect being. The cosmological proof will prove the existence of whoever created the world. The physico-theological proof will prove the existence of whoever designed the complexity of the world—the engineer, yes? The proof from morality will speak about whoever gives validity to the laws of morality. The proof from tradition will speak about whoever created the world or was revealed at Mount Sinai, or whatever the religion may be. Can you hear me? For some reason my Zoom just got disconnected. Now you can hear me. Okay, wait. Okay, so I started out speaking about six ways to arrive at belief, and I’m saying that each of the ways proves the existence of a different being. In each such path you have to define who this being is whose existence we want to prove. Beyond that, one more comment: this doesn’t mean, of course, that there are six gods—there are more; those are just six types—but there are more arguments than six. Still, it is certainly possible that each type of argument proves the existence of the same being, the existence of that same very being, but from a different aspect. One can say that the same one who gives validity to the laws of morality is also the one who created the world and was revealed at Sinai, and is the perfect being, and designed the world as reflected also in its complexity, and so on—and that this is one and the same being. It’s just that each time we prove its existence from a different aspect. It has the aspect of being the perfect being; it has the aspect of being the one who gives validity to moral laws; it has the aspect that it created the world, and so on. So the fact that we have beings here that are defined differently doesn’t mean that we are talking about different beings. Maybe even more than that: Ockham’s razor, yes? We prefer the simplest theory possible, or as few entities as possible, and therefore Ockham’s razor basically says that if I already accept—say I accept all six proofs—then it is likely that we are dealing with the same very being, just different faces, different aspects of it. Beyond that, if that’s so, then the different proofs can also strengthen one another. In other words, if I accept three of them, or six of them, that strengthens the case even beyond the force that each one has separately. Of course, there can be a person who says: I don’t accept the first proof, I accept the second; I don’t accept the third and fourth, but I accept the fifth. He accepts the first and the fifth. Fine, then he has proven the existence of God by those two means. The other ways, from his point of view, are not plausible, they didn’t convince him. Still, that is enough to reach the conclusion that God exists. So that, basically, is the overall picture. It more or less sums up the general framework, and now what I want to do in the rest of the time—and this will take us quite a few sessions—is to flesh out what I just said. To start walking path after path and see how, in the end, one arrives at God, and finally to connect the philosophical God we are discussing here to the religious God. That is, how from here we get to religious faith, to religious commitment—which is another whole story. I’ll begin with my Freudian slip, that every time I talked about seven ways to arrive at the existence of God I listed only six. Because there is a seventh way, and I’ll begin with it. The seventh way is Pascal’s wager. I don’t really include it among the paths because in my opinion it’s just a mistake, but quite a few people use Pascal’s wager and discuss it, so for the sake of completeness I want to mention it. Pascal was a philosopher, mathematician, statistician, physicist, and French theologian from the seventeenth century—Blaise Pascal. He was also a witty man, not just some heavy theologian. What I always knew from Mark Twain—one of those lines—the source is Pascal. He’s the one associated with the letter: “I didn’t have time to write you a shorter letter.” So that, originally, is Pascal. In any case, this fellow lived thirty-nine years, like many people of that period—life expectancy was low—and still managed to do quite a lot in those thirty-nine years. And as I said, the range of his expertise and occupations was very broad, but I think that’s just the nature of the period. In our time specialization has become so great that it’s hard to be a professional in so many fields. But once upon a time, whoever dealt with philosophy also dealt with science, and also with theology, so being a Renaissance man was not all that rare. At the age of thirty-one, out of his thirty-nine years, Pascal underwent some kind of very powerful religious experience—a reborn, as our cousins call it. And he returned to the religious world and to engaging in theology and so on. He presented the argument that later came to be known as Pascal’s wager as an alternative to the need for a proof of God’s existence. He says: you don’t need proofs that God exists; I can present you with a statistical argument that makes proofs unnecessary. One should remember that he is one of the founding fathers of the field called statistics, which makes it all the more surprising just how flawed this argument is—a failed statistical argument from one of the fathers of the field. In any case, his argument gets a great deal of scorn, and to a large extent justly, from many directions. Look, for example, I’ll share with you a passage from Dawkins, who very much likes to mock this kind of argument. This is a quotation from Dawkins’ book: Even if the odds that God does not exist are very high, there is an even greater asymmetry when one considers how severe the punishment would be if that guess turns out to be wrong. Better that you believe in God, because if you are right there is a chance that you will gain eternal happiness, and if you are wrong it doesn’t matter anyway. By contrast, if you do not believe in God and it turns out you were wrong, you will be damned in hell forever; and if you are right, it won’t make any difference. On the face of it, the decision is clear: believe in God. In other words, what he presents here is basically a statistical argument. He calculates the expected payoff I’ll have if I believe in God. So let’s assume I believe in God and calculate the payoff from that direction. If I believe in God, then on the assumption that there is a God, of course the reward is enormous: I gain eternal bliss in the world to come. If there is no God, then I did silly things in this world, but not terrible things happened; fine, I lived a somewhat foolish life. So overall the expected payoff is immense. If we sum up that infinite payoff multiplied by the probability that God exists—say fifty percent, doesn’t matter right now—plus fifty percent times a small loss, namely that if there is no God then I lived foolishly, overall I get a very large expected payoff. What happens if I decide not to believe in God? Then if God exists I get a terrible punishment forever—I’ll roast in hell forever—an awful and eternal punishment. And if there is no God, then I lived nicely, there is no God and I enjoyed this life—a small gain or small benefit. Overall the expected payoff is very, very, very negative. Therefore, he says, the expected payoff of belief in God, of commitment to God, is much greater than non-belief in God, and therefore: believe in God. That, basically, is Pascal’s argument. Now this is fundamentally a probabilistic argument. Why? It’s exactly… prisoner’s paradox. In any case… It’s exactly the prisoner’s paradox. Why? Which prisoner’s paradox? The prisoner’s dilemma? Yes, because if in one case it’s better to choose A, and in the opposite case it’s also better to choose A, then it’s better to choose A. Right, but that’s not a paradox and it’s not the prisoner’s dilemma. That’s what is called a dilemma argument, not the prisoner’s dilemma. A dilemma argument in logic is a valid argument—quite the opposite. One of the ways to prove a claim P is to say this: if X then P, and if not-X then also P. Conclusion: P. Obviously P is correct, because whether X is true, then P is true, and whether X is not true, then P is true. But either X is true or X is not true, so the conclusion must be that P. That’s a valid claim. A valid argument. It’s called a dilemma argument, and not “dilemma” in the sense that I’m in a no-win situation, but a dilemma argument in the sense that both horns of the dilemma lead to the same place—yes, all roads lead to Rome, so no matter which road you take, in the end you get to Rome. Okay? That’s a valid logical argument. In any case, Pascal is doing a probabilistic calculation here. He calculates the expectation—the probability that God exists times the payoff in that option, plus the probability that God does not exist times the payoff in that option—sorry, compared to the probability that God exists and that God does not exist times the expected payoff of that, and he chooses the one with the greater expected payoff. And here, of course, the first criticism of Pascal appears, namely the criticism of pragmatism. Basically, this isn’t a philosophical argument; it’s a pragmatic argument. I don’t believe in God because it’s true; I believe in God because it’s useful. It gives me a bonus, gives me a benefit. Right? It’s not an argument in favor of God’s existence. But here—notice this—Pascal himself was aware of that very point. That was precisely what he said. He was trying to render the proof of God’s existence unnecessary by saying: leave it alone, don’t get into philosophy. It doesn’t matter whether you reached the conclusion that God exists or doesn’t exist; behave like a religious person, because you’ll gain a lot from it. Right? Come spend Sabbath with us, see what a wonderful Sabbath table there is, come light candles because you’ll feel great. Right? That’s basically the Pascalian argument. Don’t believe in God—light candles, because every woman and daughter lights Sabbath candles. And that’s a pragmatic argument because it tells you: be religious because it’s pleasant, because it’s useful, because it gives you some benefit, some value—not because God really exists and really ought to be worshipped. It’s a pragmatic argument, and I already said earlier that pragmatism is not philosophy. Beyond that, Dawkins himself argues as follows, another quote from his book: Faith is not something one can decide to perform as a matter of policy. At the very least it is not something I can decide to do as an act of will. I can decide to go to church and I can decide to recite the Nicene Creed—yes, that council at Nicaea that formulated the principles of Christianity. And I can decide to swear on a stack of Bibles that I believe every word written in them. All these are acts, but none of them will cause me really to believe if I do not believe. Pascal’s wager can serve, if at all, as an argument for pretending to believe in God. And it would be best if the God you claim to believe in is not the omniscient type of God, because He will immediately discover your pretense. In other words, he is basically saying: you can pretend that you believe in God, but you cannot come to believe in God through an argument of this sort. Because if you do not believe in God, then you do not believe in Him. The fact that it’s worthwhile to believe in Him does not mean that the true conclusion is that one should believe in Him. Like when people come to someone and say, come light Sabbath candles, keep the Sabbath because your life will look so much better—that’s irrelevant, because it cannot bring him to believe in God. That’s the pragmatism I talked about earlier. But Dawkins’ same argument can also be used from slightly different angles—not only in the sense that this is pragmatism and not philosophy. In arguments… yes, I spoke in previous series about the fact that regarding factual claims there is no authority. Yes, you can’t come to me and say: accept that X is true because I am the authorized person, as with Maimonides’ thirteen principles of faith. You’re supposed to believe in those principles because Maimonides is the one who determined them, okay? And therefore the messiah will come, or therefore this Torah will not be replaced. Well, “this Torah will not be replaced” is not necessarily a factual claim, but “the messiah will come” is a factual claim. So… It’s irrelevant, because with a factual claim either I believe it or I don’t. And if some authority figure orders me to believe something, that is irrelevant. If he persuades me, then I really believe it, but if not, I can recite from the lips outward that I believe, but I cannot believe because of that. Because if the fact is that I believe, then I believe, and if not, then not. An argument from authority can instruct me to do actions. For example, the Sanhedrin tells me that sorting is forbidden on the Sabbath. In my opinion, sorting is not one of the thirty-nine primary categories of forbidden labor, let’s say. So they tell me, fine, but the Sanhedrin is authorized, and you are obligated to follow what it says and not sort on the Sabbath. That is a legitimate claim. That is a claim one can make. Why? Because I can refrain from sorting on the Sabbath even though I think there is no prohibition in it. But I cannot believe in the coming of the messiah even though I think he will not come. If I think he won’t come, then I do not believe that he will come. You cannot demand that of me by authority. One cannot demand of me by authority to think that certain facts are true if the truth is that I think they are not true. In that sense, Pascal’s argument does not come from authority, but it says: because it is worthwhile for you, therefore believe that this fact is true. I cannot believe that this fact is true if I think it isn’t. Okay, so that is very similar to Dawkins’ attack, really. He says: this is a factual claim. On the other hand, Pascal can say: okay, but you can conclude that you should start observing commandments even though you don’t believe. At least it’s worthwhile to observe commandments. Here, of course, there is an assumption that observing commandments without faith has value. I, for example, think it does not. I think there is no value whatsoever in observing commandments if it does not come out of faith. Practical implication for all those who put tefillin on people in the street: if the person you grabbed in the street is a non-believer, then if he puts on tefillin he has not performed any commandment by that; it is devoid of any religious value. Therefore this option of bypassing the need for a discussion about faith and focusing instead on commitment to observance—if I am right—does not exist. Because one cannot observe commandments without faith. This is Ahad Ha’am—I’ve mentioned this more than once—Ahad Ha’am who said that more than the Jewish people kept the Sabbath, the Sabbath kept the Jewish people, and therefore it is worthwhile for us to observe the Sabbath because it will increase our national cohesion, create connection to culture, heritage, previous generations, and so on. All that is very nice, but keeping the Sabbath it is not. Therefore that option falls away. But it seems to me that Dawkins misses something very fundamental here. When human beings discuss questions—especially questions of this sort—there is no binary state of either I believe or I do not believe. There are considerations this way and considerations that way, and in the end a person has to locate himself on the axis of how much he believes or does not believe. How strong the arguments for belief or against belief seem to him. Dawkins himself, by the way, builds some kind of seven-level scale: who is an absolute atheist, who is almost absolute, who is fairly atheistic, who is undecided fifty-fifty, fairly believing, very believing, and one-hundred-percent believing, completely believing—something like that. There are seven levels, and he places himself at level two. A scale that, I think, is six—yes? Two from the end. Meaning, he cannot say that he is an absolute atheist because he has no proofs that there is no God. He only claims that there is no indication that there is. Therefore he says that he does not take seriously the possibility that God exists, although he cannot be one-hundred-percent certain. So he places himself on level six. Thus he himself understands that there is a continuum of levels of belief in God. A person does not believe in God one hundred percent, and probably also does not deny Him one hundred percent. You are somewhere on that continuum, and each person depends on how persuasive the different arguments or directions are to him. And here, if I really am uncertain on some level whether God exists, then it is no longer completely obvious that calculations of expected payoff are irrelevant and merely pragmatism. If I think—look—there is a 50-50 chance that God exists or does not exist. Suppose. Let’s say it’s 50-50. Then Pascal can come and say, listen, then it’s worth your while to behave as if you believe in God, because your expected payoff is positive in that direction. And then you’ll ask: but will God accept that kind of observance? I think yes. Why not? After all, in the end I observe on the possibility that God exists; I am not merely doing it outwardly. I’m not sure, because no person can be sure. Every person has some level of doubt. In the end you have to decide what you’re going with. So I go with belief in God on the possibility that God exists. I have fifty percent in that direction, or seventy percent in that direction, or twenty percent in that direction—I don’t know how much. Everyone has some level of doubt. Rabbi, aren’t you distinguishing between positive commandments and prohibitions? No. Because if a person keeps prohibitions, then even if he’s not sure whether there is a God or not, in any case he won’t receive punishment for that. He… Yes. In that sense there is a difference, נכון. But there is no reward for refraining from prohibitions. Reward is for positive commandments. Yes, you’re right. That’s a valid comment. In Christianity I don’t think they make such a distinction. I don’t think there are really positive commandments there, there are hardly any commandments there. But yes, that’s a correct point. In any case, this dichotomous picture, as if I either do believe or do not believe, takes us back to the discussion I had about whether certainty is possible in belief in God. And my answer is no: certainty is not possible in anything. I mean, even in that very principle certainty is not possible—not even in the principle that there is no certainty in anything. So in belief in God too there cannot be absolute certainty, and everyone has a certain level of doubt, and one has to conduct oneself in everything. A person has doubt about everything, and nevertheless he makes value decisions and others—economic decisions, whatever you like. I make decisions under conditions of uncertainty, so with regard to belief in God too I am supposed to make decisions under conditions of uncertainty. And a person can decide this on the basis of pragmatic considerations. Therefore I do not reject this Pascalian direction when I remember that belief in God is not a binary matter, but rather there is fuzzy logic here, yes, some continuum of levels of belief in God between zero and one. And a person is somewhere in the middle and calculates expected payoff. What would a person do who is at the far left end of the scale? He thinks there’s only a ten percent chance that God exists—like Dawkins—he’s very low on the scale. So does Pascal’s calculation still produce the same result? Pascal himself senses this and claims yes. Why? Because the reward for observing the commandments of the Holy One, blessed be He, is so great and eternal—it is truly infinite—that even if we multiply it by ten percent or by one percent probability, the expected payoff is still immense, infinite if you like. And the punishment is so terrible on the other side that it doesn’t matter at all what the probability is that you will receive punishment—in the end it is always better to observe commandments than not to observe commandments. Therefore Pascal basically claims that because the reward and punishment are infinite, the wager argument does not depend on the probability that God exists or does not exist. Even if the ratio is ninety-nine percent to one, or ninety-nine point nine nine nine nine percent to one, still the calculation stands. So Pascal argues, and therefore it has nothing to do with where you are on Dawkins’ scale. Even Dawkins himself should observe commandments, Pascal claims. And therefore all the usual arguments against Pascal, in my opinion, do not really hold water. Why did I say that I disagree with Pascal and that he is talking nonsense? Because there is one argument that I have not seen anyone raise, for some reason. Maybe someone has, I don’t know, but I haven’t seen it. And in my view it is the decisive argument. And this argument attacks Pascal’s reasoning precisely on the statistical, probabilistic plane—not on the theological planes and all the arguments we’ve discussed until now, whether it’s a fact or not a fact. He is probabilistically mistaken. And here I want to give a few examples to sharpen the point. Suppose someone offers you a coin-toss lottery. And this coin is biased. Okay? There is a ninety-nine percent chance it will land heads and a one percent chance it will land tails. They tell you this in advance; it’s not cheating. They tell you beforehand. And they say: look, if it lands on tails… sorry, the opposite. The probability is ninety-nine point nine nine nine nine—yes, four digits after the decimal—that it will land heads, and ten to the minus four that it will land tails. Okay? Now if it lands on tails you’ll win, I don’t know, ten to the hundred dollars. Fine? And if it lands on heads you win nothing. How much money would you invest to buy a ticket for this lottery? The expected payoff of this lottery is enormous. Do the calculation. There is the probability of winning nothing, ninety-nine point nine nine nine nine—that contributes zero—plus the probability of ten to the minus four of winning ten to the hundred. That is ten to the ninety-six dollars, a number of dollars that never has been and never will be in existence—that is an imaginary quantity of money. People perhaps are not sufficiently aware of exponents, but ten to the ninety-nine is a fictional number. That is a ten with ninety-six zeros after it. Fine? In dollars. That is the expected payoff of the lottery. Now I’m offering you a ticket: how much would you pay? Almost nothing. Ten dollars. Would you pay a thousand dollars? The expected payoff is enormous, much more than a thousand dollars. Maybe for one dollar you might buy it for fun—maybe after all we’ll win. But if the price were such that it would involve a significant loss—I offer it to you for a million dollars. Sell the house. Look, but your expected payoff is enormous. No sane person would do that. Why not? After all, expected-value considerations show us that the price here is much more than a million dollars. Why not sell everything I have and buy a ticket to this lottery? So in investment courses, in economics courses, they illustrate this phenomenon—the problematic nature of the expectation criterion—through what is called the St. Petersburg paradox. I’m now offering you something very similar. Earlier I offered you a simple heads-or-tails lottery with a biased coin. Now I’ll offer you what is done in the St. Petersburg paradox. Look. I offer you the following game. Let’s toss a coin. If it comes up heads, you get two shekels and the game ends. If it comes up tails, we toss the coin again. If it then comes up heads, you get four shekels and the game ends. If it comes up tails, we toss again; if it comes up heads, you get eight shekels; if it comes up tails, we toss again and the game continues. If it comes up tails, toss again: sixteen shekels, powers of two—yes? Two, four, eight, sixteen, thirty-two, and so on. Okay? Now I offer you this game. How much would you pay for a ticket? So now we’re already experienced, right? So let’s calculate the expectation. I’ll show you the diagram that illustrates this. Look. Can you see the diagram? So here, I toss a coin. If it comes up tails, I earn two shekels, and the probability is one half, right? Probability one-half, either heads or tails. So with probability one-half I earn two shekels. If it comes up heads, I toss again. If it comes up tails, profit of four shekels, and the probability of that is one quarter, because the probability of getting heads at the beginning is one-half, and the probability of getting tails afterward is another one-half, so the probability is one quarter. Okay? If it comes up heads, we toss again. If it comes up tails, profit of eight with probability one-eighth. If it comes up heads, toss again; tails gives profit with probability one-sixteenth; heads and so on, continuing onward. Notice the bottom line of this game. The game can end either here, or here, or here, or here, and of course so on to infinity. So that means that with probability one-half I get two shekels. With probability one-quarter I get four shekels. With probability one-eighth I get eight shekels. With probability one-sixteenth I get sixteen shekels. Add up all those probabilities and you get one, right? One-half plus one-quarter plus one-eighth plus one-sixteenth and so on to infinity—that equals one. It’s an infinite series that converges to one. So that marks all the possibilities for ending the game. What is the expected payoff in this game? We already know how to calculate it. One-half times two, which is one, plus one-quarter times four, which is one, plus one-eighth times eight, which is another one, plus one-sixteenth times sixteen, which is also one, and so on. Meaning, this is one plus one plus one plus one plus one and so on to infinity. The expected payoff of this game is infinity. The expected payoff of this game—the average gain for someone who plays this game enough times—is infinite shekels. So if that is so, then it is worth investing any amount in this game. If I offer you a ticket for a million dollars, a hundred billion dollars, whatever you have—it is worth investing, because the expected payoff is infinite. How much would you invest? I offer you a ticket to this game. How much would you give me? Would you give a thousand dollars? I wouldn’t. Never in my life. Maybe I’d give five dollars, I don’t know, ten dollars. That’s the order of magnitude, and even that I’d give reluctantly; better to buy a popsicle. So what’s the idea? After all, the expectation criterion… only if you do it enough times. Exactly. So what they illustrate to investors is this: what is expectation? Average profit is always the profit obtained on average when I play the game many times. If I play this game many, many, many times, here I’ll gain one, here I’ll gain three, here I’ll gain two; on average the profit will be infinite. Not cumulative—average. Notice, I’m not cheating completely. It’s not that obviously if I play it infinitely many times I’ll earn infinitely much—that’s trivial. But if I play it infinitely many times, the average profit per game will be infinite. That’s the average profit. So it’s not total cheating. The catch is that the probability in a single game of gaining that average profit is negligible. If I play this game once, until it stops—tossing the coin until it stops—just once, I have only one trial. The probability that in that trial I’ll get any substantial gain, say more than four or eight shekels, is very small. You’ll never get to a thousand shekels. You won’t get there—the probability is tiny. And it turns out there is an interesting statistical phenomenon that says the average profit is not always the expected profit in the sense of what is likely to happen. The profit likely to occur, the plausible profit, is the typical case. Here infinity is indeed the average profit, but it is not the typical profit. The frequency of that profit is very, very small—essentially negligible. So basically they are offering you a lottery—let’s go back to the single coin I talked about at the beginning—a coin where with probability ten to the minus four you win ten to the hundred, and otherwise you win nothing. So yes, the expected payoff is enormous, but what is the probability that I’ll reach that average payoff? I toss the coin once. Either it lands heads or… it will never land tails, there is no chance it lands tails in practice. The probability that it lands tails is one in ten thousand. It won’t happen. We go out on the road where our chance of being killed is something like that, say one in ten thousand. And we go out onto the road without batting an eye; we have no problem with it, even though it’s a gamble on life. Because one in ten thousand is a chance we take easily; it won’t happen. That means expectation is a criterion, but not always a good criterion for making decisions. Expected value is a good criterion for making decisions when the average profit lies in common cases, in situations likely to occur. But sometimes there are pathological cases where the average profit is reached only in very, very rare cases. Because in those cases I will earn such a huge profit, the average profit is heavily influenced by the rare cases. But they are terribly rare—it just won’t happen. Therefore such a gamble is not worth taking. These are situations in which the distribution of possibilities is very, very asymmetric, not Gaussian. So the average profit will not occur. What does this have to do with us? I return to Pascal. Suppose Pascal comes to persuade an atheist to observe commandments and believe in God. Now this atheist is an honest atheist. He understands there is no one hundred percent here. You can’t be certain that there is no God. So Pascal says to him: good, then let’s do the expected-value calculation. So the atheist says to him: yes, but for me it isn’t fifty-fifty; for me it’s one in ten thousand against ninety-nine point nine nine nine nine. Pascal tells him: what difference does that make? The payoff is still infinite, so the expected payoff is still positive even with the distribution you hold, therefore it is worthwhile for you to observe commandments. The atheist says to him: you’re talking nonsense, and as one of the fathers of probability I’d have expected even less that this would happen to you. This is exactly the probability we talked about earlier; I don’t buy a ticket to that. The payment I make—in other words, observing commandments, which bothers me—that nuisance is like buying a ten-dollar ticket to the game. I do not invest ten dollars in a game in which I have no chance of winning. The chance of an enormous profit is tiny. In the atheist’s eyes, the probability that God exists is tiny. So even if the payoff is enormous and the expected payoff is very, very large, the chance that I reach that payoff is minuscule. I don’t buy a ticket to such a lottery—not even for a thousand dollars. There’s high risk here. The risk is high, like with a lottery ticket—I didn’t buy it. Same thing: the high risk and the high payoff are both irrelevant, because they occur with extremely small probability. From the atheist’s point of view, the probability that God exists is tiny and the probability that God does not exist is almost one. So yes, if God exists then he’s in huge trouble, but that side is, in his view, very very improbable. So there is no reason to buy a ticket for such a lottery. It’s not worth investing even the effort of observing commandments in your life—which is not impossible effort, true, but still—not worth investing that in a lottery where you have no chance of winning, or where your chance of winning is negligible. On the other hand, if there is a lottery with a prize of a hundred million shekels, everyone in the country will buy a few tickets. Therefore—that is why I prefaced this by saying—but if someone offered you to invest half a million dollars in it? No. If you invest ten dollars, you’re doing it for sport—maybe the small chance will happen and I’ll win. True, the expected payoff is still negative, but fine, there is some chance I’ll get a million dollars, and ten dollars is not a price, from that point of view. So I’ll invest ten dollars. But as I said, I’m talking about a price I don’t want to invest. Yet expected value tells me I should. I say: yes, but I’m not going to win in this game, so I’ll just be left with the loss of the ticket price. A thousand dollars is already a meaningful price for me. That I won’t invest. That’s a utility function, basically. A person calculates for himself how much a thousand dollars is worth to him. My thousand dollars and your thousand dollars are not the same thing. If I’m Bill Gates, then my thousand dollars is like, I don’t know, a cent to someone else. He doesn’t feel a thousand dollars. So maybe he would also invest a thousand dollars in this amusing game. But if I offer him a lottery that even for him has a meaningful price, then he won’t enter it. So let’s talk about a ticket price that is meaningful for you. Let’s not talk in absolute numbers. Each person and what is meaningful for him. Even though in terms of expected payoff both Bill Gates should invest a million dollars and I should invest my dollar to the same degree, because it’s an infinite payoff. But if the price is meaningful for us, we won’t enter that lottery, even though the expected payoff is infinite. So keeping commandments—how much is the price? One person says: fine, so I’ll keep them, I don’t care. But the atheist says: keeping commandments, for me, is a heavy price. To be in synagogue three times, one day out of seven not to travel, not to have any fun, not to eat non-kosher, all the things I’m used to—that’s a sufficiently significant price. You can stand it, true. If someone told me, you will definitely die, then I would do it. But if someone tells me: look, you’ll die but with probability one in a million—then leave me alone, I’ll take that chance. I take that risk, just as I go out on the road to drive. There is some risk that I’ll die. And I don’t like gambling with my life, but with a risk of one in ten thousand or one in a hundred thousand, those are risks we take every moment. It’s not a big deal. Even though not driving a car is not such a heavy price, it’s a smaller price than living observantly your whole life. So don’t drive a car—take the bus, walk on foot, at least when you don’t have to. What’s the problem? You’re gambling with your life. And the fact is that we all do it. We all do it because the probability is very small, and we are not willing to subject our lives to a tiny probability. And that is rational behavior. There is nothing irrational here. It’s not that I pointed to an irrational aspect of our behavior. This is rational behavior. Therefore I think that Pascal’s wager is mistaken not in the statistical calculation. The expected-value calculation may be correct. Rather, it is mistaken in decision-making. And that is the miss that existed in Pascal. In making decisions one must know that the expected-value criterion is not always a good criterion by which to make decisions. When the expected value is the typical case, then it is a good criterion. When the expected value appears only in atypical cases, in a very very asymmetric distribution or one very heavily skewed to one side—in such cases, do not go by the expected-value criterion. The expected-value criterion is a very poor criterion. Someone tells me: I heard there is a treasure of billions upon billions of shekels and diamonds on some island in the Pacific Ocean. Fine? So let’s outfit a ship, hire sailors, sail there for a year, dig there, and you know what? There is a one in a billion chance that it’s true. And the treasure is billions upon billions, so the expected payoff is a billion. Right? One over a billion times billions upon billions is a billion. So how much will it cost me to outfit a ship? Ten million? A year of travel? The expected payoff is still enormous. Would you go on such a voyage, such an adventure? There is a one in a billion chance. Why not? Because the probability is very, very small, so what if the expected payoff is huge? The chance is tiny that it will happen; I just wasted a year of my life and money. There are people who do that, though. Depends. I think there are no people who do that unless they enjoy the process, but there are people who enjoy taking the risk and outfitting a ship and doing the experiment. They’re not doing it for the payoff; for the payoff, no rational person would do it. You know, it’s like a lottery ticket. Ask a statistician whether it makes sense to buy a lottery ticket, any kind of ticket. A responsible statistician will tell you: I cannot answer, it depends on your utility function. What do you mean? The expected payoff is certainly negative. So what? The point is that there the expected payoff is negative and the probability that the gain will happen is tiny, so both considerations are against buying a ticket. It’s not that I presented a situation where the expected payoff is positive, only the probability is very small. In the lottery it’s even much worse than Pascal’s wager, because in the lottery the expected payoff is also negative and the chance it will happen is also very, very small, so there is no reason in the world to buy a ticket—and the fact is that many people buy tickets. Why? As I said: first, because the investment is very, very small. You buy it for a few shekels, fine, let the tiny chance go, who cares? Overall I only lost a few shekels, it’s not terrible. Beyond that, some people like the suspense—they enjoy waiting to see whether I’ll win or not win, maybe I’ll win—they are paying for that, not for the payoff at the end. And sometimes there are people—look, if tomorrow someone comes to me and says: look, if you don’t pay a million dollars tomorrow, we’re coming and killing your entire family. Now I have no way to get a million dollars except by buying a lottery ticket, where the chance of getting a million dollars is tiny. But that’s my only way to be saved, so I’d buy a ticket. Because I have no other way out—what can I do? Otherwise I die tomorrow if I don’t bring a million dollars. That’s my only route; if I’ll have a million dollars, only like this. So I buy a ticket at whatever price. Understand? But that doesn’t mean there really is some expected payoff by which I’m operating; rather, my circumstances are such that I have to, because the alternative is an even greater loss, and therefore I do it. But if I’m in an even situation and I’m simply weighing whether to buy a ticket or not buy a ticket, clearly I buy no ticket to such a lottery. Expected value here is not the relevant criterion. And that is exactly the situation with Pascal’s wager. In other words, I think all the previous arguments against Pascal’s wager are not correct arguments. All the arguments I’ve read in the literature—everyone laughs at Pascal’s wager—they laugh unjustly. Those arguments do not hold water. Pascal’s wager has logic from all the theological and other perspectives, except from the statistical perspective—which is really interesting, because everyone says the opposite. Everyone says Pascal’s wager is obviously statistically correct, but there are theological problems: how can I believe if I don’t believe, what good is observing commandments without belief, all those arguments are theological arguments. So the assumption is that the statistical argument is great and the problem is theology, and I argue the opposite. The theological problems are not the problem. The only or main problem in Pascal’s wager is the statistical problem, not the theological one. Okay, so if that’s so, then what? What was said is that the whole probabilistic matter concerns an infinite number of repeated actions, and that’s what they say is the difference between laboratory conditions and reality. And allow me one second—no, it has nothing to do with laboratory or reality. It depends on how many times you get to do the experiment. It doesn’t depend on laboratory versus reality; it depends on how many times you have to do this experiment. Right, but that’s the difference if you live infinitely many times, and each time you can bet on whether there is or isn’t a God—go with the wager that there is a God, Pascal is right. No, I just want to explain in reality—an actual story happened to me—the difference between laboratory conditions and reality. We were once in a casino in Las Vegas, and before that on some flight there was someone who told us how he beats all the casinos in the world and all that, and we said okay, we’re going with this. There you have red or black, let’s say, two options to choose from. Statistically that’s fifty percent, no? So we said we’ll bet on red. It didn’t work, so we bet again with a doubled amount. It didn’t work, so we double the amount again. In the end red has to come up, so if each time I double… one hundred percent I win, right? It can’t be that… It’s a known argument, known method. Theoretically that’s true. It’s a known story. But what? Here’s reality. I do it again, we lose, and again we lose. You increase the amount, you panic, you break. And the fact is that in the end we stopped because we got scared. I think that’s not a difference between laboratory and reality. Obviously human psychology enters in, but in that case you really will profit in the end. If it really is a fifty-fifty chance between red and black, that’s a simple case where you really will profit in the end. That’s just psychology. But the question is whether the chance there really was fifty-fifty between red and black; you have to examine the case itself. Anyway, for our purposes, maybe I’ll tell one more story to conclude. I hope I have a few minutes left, and with this we’ll finish Pascal’s wager, because we’ll take it off the map of possible ways to arrive at faith. That’s what I did in this session: I removed the seventh possibility. We’re left with the six I listed earlier. One last story to end with. I’ve told it more than once. Once, when I lived in Yeruham, we drove with the family to some family celebration. Yes, six children, two parents—we drove, we had a large car, we drove to Kfar Chabad. We returned, it ended, and at one in the morning we were coming back via Gedera. Some young woman came out from the side, the guy in front of me braked, I hit him, and then the bus came. This was one in the morning in Gedera, while I’m on the way to Yeruham with my whole family, with six children. Okay? Boom. Before I even manage to understand that there was an accident here, a large empty vehicle stops beside me, one that can hold all of us—belonging to a neighbor of mine from Yeruham. We all got into his vehicle, drove off, left the key at some kiosk that was open nearby, and drove to Yeruham happy and cheerful. What did I say to the guys at the Friday-night gathering in the yeshiva afterward? I said to them: so now I’m supposed to thank and praise the Holy One, blessed be He, for the great miracle He performed for me? It’s unbelievable. What’s the probability that such a thing would happen? Think about it: I’m stranded in Gedera with eight people in the middle of nowhere with a disabled vehicle. How do I get to Yeruham? Order two taxis to Yeruham at an enormous cost? I don’t know how to order them; I think we didn’t even have a cellphone then. In short, the story is hopeless. We get into my neighbor’s vehicle. It turns out he was a local politician in Yeruham, and he was used to driving the Yeruham-Jerusalem route all the time. He had business there; he knew that route by heart. He says: I don’t know what happened this time, I got confused, missed the turn there at Latrun, and somehow ended up in Ramla, in Gedera. I don’t know these places at all. Suddenly my wife says to me—this is what he tells us when we got into his car—suddenly my wife says to me, look, there’s the Abraham family. Stop for them; maybe they need something. Now understand, this was at the exact moment of the accident. Meaning, he hadn’t even seen yet that there was an accident, and we ourselves still hadn’t understood what had happened. He says, okay, fine, the Abraham family—so what? Who says they need me at all? She says, no, no, stop, maybe they need you. So he stopped, and indeed we needed him. And he had a large vehicle, not a small one, and all eight of us got into it and drove to Yeruham. I won’t lie to you that we were all buckled in, but all eight of us got into that vehicle and drove to Yeruham. What is the probability that such a thing would happen? Tiny—a revealed miracle. I said to the guys in the yeshiva, look, I don’t know what the probability is that this would happen. Let’s say the probability is one in, I don’t know, ten thousand—just for the sake of the game. I didn’t check ten thousand cases in which people got stuck in the middle of nowhere with eight people and no way to get home. Okay? Since that’s the case, I cannot know whether what happened here departs from the statistics or not. After all, one case out of ten thousand is supposed to happen. And someone will be that one person to whom this case happens. So that someone is me. Any improbable event, if it happens enough times—and after all, accidents and someone getting stuck at night do happen more than once; these are things that have happened many times all over the world. Now, I didn’t do a statistical study of all those cases and check in how many of those cases a neighbor of the person stopped with a large vehicle and picked him up. It could be that in one out of ten thousand cases that happened, and the chance of it happening is one in ten thousand, and everything is fine; there is no miracle here. You know, there is a book called Think of a Number by John Verdon, some thriller, and it begins like this. You receive an envelope, and inside there is a letter and another little envelope. In the letter it says: open the envelope, think of a number between one and… a thousand. Open the little envelope, and you will see inside the little envelope the number you thought of—I know it in advance. If I’m right that inside the little envelope there is the number you thought of, send me, I don’t know, $1,000 or $10,000, and I’ll make you a billionaire. Look, I have supernatural powers; I can know what you’ll think of, so it’s worthwhile for you to invest in me. Fine. I open it, I think of the number 771. Fine? 770, close enough. I open the little envelope—unbelievable—it says 771. Immediately I run to send him $10,000, to this all-powerful person who’ll make me a millionaire if he is so all-powerful. What turns out at the end of the book? He asked for only 1,000. What? He asked for only 1,000, don’t send him 10,000. I can’t hear. He asked for only 1,000—don’t send him 10,000. No, he asked… He sent 10,000 letters like this; the stamp cost him a quarter. Exactly. Meaning, he sent 10,000 letters, and tells everyone to choose a number between one and a thousand, so he has a random chance of hitting ten choices. Those ten choices will each send him 10,000 dollars, giving him 100,000 dollars. Sending 10,000 letters will cost him, I don’t know, 2,000 dollars; he earned 100,000 from the 2,000 he invested. When I got the letter I was sure he was all-powerful, but I didn’t check what happened to the other 10,000 people who got the same letter and whom he didn’t convince. That is what alternative medicine is built on; that is what all the Oren Zarifs and all the charlatans are built on—those who manage to guess your illness and cure it—because there are another 10,000 people like you for whom they did not succeed. It’s just that no one did the statistics; only the successful cases get publicized. Okay? So that’s the statistical miracle. I once called it the law of small numbers. There is the law of large numbers, and there is the law of small numbers. With small numbers, any prediction can work—that’s a law in statistics. Therefore one must beware of statistical probability when one is not sufficiently familiar with the general sample space. As someone remarked to me in the chat—yes?—it’s not worthwhile to thank the Holy One, blessed be He, for that, because He is also the one who caused me to have the accident. I already talked about whether one should thank Him for it because of the question whether there was a miracle here. On that argument I completely agree. The fact that He saved me is true, but He also got me into the mess, so what have I gained one way or the other? Enough. I can’t hear. I argue that it wasn’t God who caused the accident. So I can’t hear. I argue that it’s a response to the opposite intuition: it wasn’t God who caused the accident; the accident was caused by the person who drove the vehicle. Okay, and God also didn’t send my neighbor; rather, my neighbor got confused and arrived, in the same way. That’s a different question. Why is that a different question? It’s the same question. If you decide that God does what people do, then He did both things. And if He didn’t do it, then He didn’t do both things. Why decide that He didn’t do the first but did do the second? Okay. Rabbi, Rabbi, can I ask something? The question is whether the comparison we made between probability in terms of money—an infinite financial return—and the risk a person takes regarding something spiritual, hell, things like that—maybe there the ratio between probability and risk is different. Because the good spoken of there is something infinite, and likewise the bad, whereas with money, fine, so I’ll have all the money—so what am I going to do with it, really? No, that already depends on what I called earlier your utility function. But let’s say that even if your utility function treats that as something with infinite payoff, still, if the chance of getting it is very small, there is no reason to take it. If you desperately want it, then from the standpoint of your utility function maybe it will work on you, I don’t know. But there is no statistical necessity to accept Pascal’s wager. As I said with the lottery ticket: there is no reason to buy a lottery ticket, because both the expected payoff is negative and the chance that it will happen is very, very rare—it’s even worse than Pascal’s wager. Yet people do buy them. Why do they buy them? Because they like the risk, or because they want, all the same, that remote possibility of winning a million dollars. But they aren’t doing it for the payoff. That’s what I earlier called a utility function. So there may be a person whose utility function is such that it is worth it for him to take even a gamble with a very, very small probability in exchange for infinite spiritual gain or to avoid infinite spiritual loss. But that’s your utility function. It’s not universal. It’s not something that can persuade every person on the probabilistic level. Fine. And before Yeruham we were on Carmel Center, Bikkurim Street… What? I can’t hear. I’m saying, before Yeruham. What, where did you live? Right, so my sister lives there. Okay. So my nephew tells me he knew your father. Fine. Okay. Small world, yes. Well then, goodbye, have a peaceful Sabbath. A peaceful Sabbath, and thank you very much. Same to you, a peaceful Sabbath.