Doubt and Statistics – Lesson 26

Table of Contents

• Statistics versus human behavior, determinism, and randomness
• Van Inwagen’s argument and introducing the concept of “reason” as a third category
• David Hume, the problem of causality, and the status of experience in relation to randomness and choice
• Randomness as a mathematical model: coin tosses and dice as deterministic processes, and statistics as a description of human initial conditions
• Maimonides, Laws of Repentance 6:5: prophecy/decree at the collective level versus personal responsibility
• A critique of the Raavad’s solutions and a proposed statistical model for Maimonides: a “statistical decree” and weighting the scales
• The law of large numbers, independence, and the paradox of prediction emerging from the freedom of individuals
• Free choice is not an equality of forces: practical difficulty, responsibility, and application in situations of social dependence

Summary

General Overview

The text argues that the ordinary use of statistics assumes randomness, but human behavior is not random; it stems either from determinism or from free choice, and therefore, at least on the face of it, statistics should not really apply to it. It rejects Peter van Inwagen’s dichotomy and proposes a third distinction between cause and randomness through the concept of “reason,” which allows for action that is neither caused nor random. From there it arrives at a paradox: in practice, statistics is almost always applied to deterministic or human processes, not to genuine randomness. It then uses Maimonides (Laws of Repentance 6:5) and the discussion with the Raavad to propose a model in which a collective decree or prophecy can be fulfilled statistically without negating the choice of the individual, through a biasing of the “weights” of choice and the behavior of large numbers.

Statistics versus human behavior, determinism, and randomness

The text assumes that statistics is usually understood as a tool that describes random events, whereas human behavior is not random: the determinist will see it as the necessary result of causes, and the libertarian will see it as the result of free choice. It concludes that from this perspective there should be no natural place for statistical tools in relation to human actions. It presents this difficulty as a principled problem that requires clarifying the relationship between randomness, causality, and choice.

Van Inwagen’s argument and introducing the concept of “reason” as a third category

The text presents Peter van Inwagen’s argument, according to which every act either has a cause or has no cause; if it has a cause, that is determinism, and if it has no cause, that is randomness, so there is no room for free will. It argues that the mistake is identifying “no cause” with “randomness,” because without a cause there are two different possibilities: randomness or free choice. It defines the distinction through “reason,” meaning purposive action that involves judgment and aims at achieving some value or goal, and is therefore not random even though it is not causal in the deterministic sense. It proposes a threefold division: cause (determinism), reason (free choice), and the absence of both cause and reason (randomness).

David Hume, the problem of causality, and the status of experience in relation to randomness and choice

The text adopts David Hume’s claim that observation does not provide a causal relation but only a sequence of events, and therefore causality is an interpretation rather than a direct empirical datum. It adds that pure randomness, an event with neither cause nor reason, is not something known from experience and is even hard to conceive of, and therefore such events create confusion in standard interpretations of quantum theory. It argues that of the three forms of behavior, free choice is actually what is experienced most immediately from within, and it cites Schopenhauer as someone who claims that this is the exceptional case in which one has access to the “thing in itself” when a person looks inward at himself. It concludes that preferring the determinism/randomness dichotomy while omitting free choice is not only a logical mistake but also an ignoring of the thing most familiar in experience.

Randomness as a mathematical model: coin tosses and dice as deterministic processes, and statistics as a description of human initial conditions

The text argues that tossing a coin or a die is not truly random but deterministic if all initial conditions are known, such as speed, angle, and environmental conditions; therefore randomness is a mathematical model and not a property of the macroscopic world. It argues that every statistical application in everyday life does not describe genuine randomness, and that the only exception is quantum theory in the microscopic world according to standard interpretations. It explains that the statistics of a coin toss are not about “what will happen to the coin” but about what the person actually does in the act of tossing it, meaning the variation in the initial conditions that stems from human action not precisely under control. It concludes that in practice statistics is used in relation to determinism and in relation to human conduct, even though its original definition is perceived as a description of randomness.

Maimonides, Laws of Repentance 6:5: prophecy/decree at the collective level versus personal responsibility

The text cites Maimonides in Laws of Repentance, chapter 6, halakhah 5, on “One who comes to purify himself is assisted,” and on the question of how Egypt or Israel can be punished if it was said in advance, “And they shall enslave them and afflict them,” and “And this people will rise up and go astray.” It brings Maimonides’ answer that it was not decreed against “a particular known individual,” but rather that “the way of the world” was stated, so that each individual still remains able not to choose evil even though the statement is about the collective. It also brings the Raavad’s gloss, which argues that these are “lengthy words with no substance” and “childish words,” because if the decree is fulfilled, it must apply to the ones who actually did it and not to those who did not. He adds that the Creator’s knowledge is not a decree, so there is no need for Maimonides’ answer. It also presents the Raavad’s two lines regarding Egypt: that the Creator exacts punishment for evil by means of someone more evil than the victim, and afterward also exacts punishment from the perpetrator; and that since the Egyptians “added to the evil” beyond what was stated—“with harsh labor,” “they killed,” “they drowned”—they became liable to punishment.

A critique of the Raavad’s solutions and a proposed statistical model for Maimonides: a “statistical decree” and weighting the scales

The text argues that the Raavad’s solution based on prior wickedness leads to an infinite problem of where the chain begins, comparing it to the difficulty in the Talmudic passage in Makkot 10 about an inadvertent killer who is “judged” because of previous sins, back endlessly. It argues that the solution that “they added beyond the decree” already presupposes an area in which the Creator does not dictate matters, and thereby bypasses the core of the problem. It proposes understanding Maimonides as pointing to the possibility that the Holy One, blessed be He, can determine a collective outcome without determining which individual will carry it out, by biasing the conditions of choice in the group so that the distribution of choices leans in a certain direction. It sharpens the Raavad’s objection: if it was predetermined that in the group there would be “ten” enslavers, then once everyone else chooses good, the last ones will be forced to choose evil. It answers that the mechanism is statistical and not coercion of an identified individual.

The law of large numbers, independence, and the paradox of prediction emerging from the freedom of individuals

The text uses the law of large numbers and emphasizes that it works when the trials are independent; then, precisely in the place where one cannot predict the result of a single toss, one can accurately predict the distribution over a large number of tosses. It highlights the strangeness that statistical coordination appears precisely when there is no coordination between the trials, and presents this as a fundamental feature of probability. It carries the same logic over to people: even if each individual chooses freely, in a large group one can predict the rates of choice according to the weights and tendencies, and it even argues that this is “because there is free choice” and not “despite it,” since the independence of choices allows statistical behavior. It presents the possibility that the Holy One, blessed be He, changes the “distribution” of choice by changing tendencies and environment, so that a certain collective expectation is produced, similar to turning a coin into an unfair coin so that over many tosses it will fall more often on one side, even though a single toss is still not compelled.

Free choice is not an equality of forces: practical difficulty, responsibility, and application in situations of social dependence

The text states that free choice does not mean that the options are evenly balanced or that there are no weights and constraints, but rather that the options are open in principle and there is no deterministic coercion toward one single outcome. It gives the example of provocation that increases a tendency toward violence and still does not cancel responsibility, and from this concludes that one can “tilt” circumstances so that the majority will choose in a certain direction and still judge the particular chooser. It addresses a comment about dependence and correlation under monarchic or totalitarian rule, and agrees that the law of large numbers requires independence, but argues that even under strong correlation one can predict acts of atrocity and still attribute personal responsibility to the perpetrators, similar to the argument about Nazi Germany and the Nuremberg trials. It concludes that Maimonides means a collective “statistical” prophecy and not a decree about a specific personal identity, and that this move is likely to lead to further implications later on.

[Rabbi Michael Abraham] Okay, at the end of last time I started talking a bit about the use of statistics with respect to human behavior. What exactly is the problem? Usually, when we use statistics, our assumption is that the event in question is a chance event, a random event. And random events operate according to some kind of statistics. But human behavior is not a random event; in no case, apparently, is it a random event. Determinists will say that human behavior is deterministic behavior, and libertarians—since I think I have free choice—so I think human behavior is the result of choice or free will. Either way, whether it’s deterministic or libertarian, it’s not accidental, it’s not random. And therefore, on the face of it, I would not expect statistical tools to be applicable, to be able to serve us when we deal with this kind of phenomenon. Maybe I’d sharpen this through a common objection to the idea of free will; it also came up on the site some time ago. There’s an American philosopher, I think of Dutch origin, Peter van Inwagen. And he raised an argument against the possibility that people have free choice. And his claim is basically this: if a person performs an act, there are two ways to describe it. Either there is a cause for what he did, or there is no cause for what he did. There is no third possibility: either there is a cause or there isn’t. If there is a cause for what he did, then the result or the act is determined deterministically, because the cause is a sufficient condition for the occurrence of the effect, so that’s determinism. And if there is no cause, then it’s randomness. It’s just an accidental matter. Either way, one way or the other, obviously he has no free choice. And the concept of free will has no place on this map, because if there is a cause, that’s determinism; if there is no cause, that’s indeterminism—yes, that’s randomness or accidentality—and either there is a cause or there isn’t, there is no third possibility. And there is a reason. You hear? A reason. Yes, we’ll talk about that—that’s the answer. But his claim is that since there is only either the possibility that there is a cause or the possibility that there isn’t a cause—if there is a cause, that’s determinism; if there isn’t a cause, that’s randomness, indeterminism—therefore, he says, there is no place on the map for a mechanism, let’s call it—I don’t know whether mechanism or mode of operation—of free will. It’s simply not defined. There are two possibilities here that cover the whole space. There’s no room for it. The mistake in this argument, the mistake in this argument, is that when you say that some action has no cause, or some act has no cause, that still does not mean indeterminism in that sense—meaning randomness or accidentality. It means there is no cause. There can still be two ways to describe it. One possibility is randomness—it simply happened just like that, an accidental matter. The second possibility is free choice, meaning free will. Both of these modes of behavior are behaviors without a cause. So he is right that either there is a cause or there isn’t. He is not right that once we assume there is no cause, we have arrived at indeterminism, at randomness. That is not true. What distinguishes free-will behavior from… random, accidental behavior? In this context he uses the concept of a reason. Meaning, a person’s act or decision is the result of deliberation and it has a reason. Meaning this act generally comes to achieve something. And therefore it is not an act done just like that, randomly, on the one hand; it is not random. On the other hand, there is no cause here. If there were a cause here, then I wouldn’t be coming to achieve anything. The cause simply produced this act, and that’s it. When I say that I performed some act in order to achieve some result, to advance some value, whatever it may be, that basically means there was some kind of deliberation that I engaged in when I decided to do it or to think that way. And this kind of conduct—deliberation, judgment—means that on the one hand there is no cause, and on the other hand the act is not random. It’s not accidental, it’s not just random chance. Meaning, there is actually a third category here: behavior according to a reason, and not behavior by force of a cause. So now you can divide the map not into two divisions, not into two possibilities as van Inwagen does, but into three possibilities. Either there is a cause, or there is a reason, or there is neither cause nor reason. If there is a cause, that is determinism. If there is a reason, that is free choice. If there is no cause and no reason, then that is random behavior, accidental behavior—it simply happens just like that, okay? Therefore van Inwagen’s argument is really begging the question. Begging the question in this sense: he basically assumes there are only two categories. He says that once you negate the possibility that there was a cause for what I did, you automatically arrive at randomness. And this assumption that he argues for, he is actually presupposing. Because when he argued with me about this issue, I told him: what do you mean? It’s true that there is no cause for human action, but that still doesn’t mean there is randomness here. There are two possibilities: either randomness or action with a reason. And therefore the dichotomy he creates, the two possibilities he sketches there, do not cover the whole map. Meaning, the map contains further possibilities beyond those two. Now then, we actually have three mechanisms—I’d maybe even say more than that. What is especially strange, I had a discussion not long ago with someone, what is especially strange in my eyes is that people constantly cast doubt on the possibility that we have free choice on the basis of van Inwagen’s argument, and every discussion of free choice starts with that argument. When the two possibilities they choose, which in their view cover the whole possible range, are either determinism or indeterminism, they omit the third possibility of free choice, when the only possibility that is familiar to us in what I think is an intimate and very immediate way is precisely the possibility of free choice. The other two possibilities are possibilities not familiar to us from experience. And for some reason people decide that precisely those are the two existing possibilities and ignore the third, which is the one most familiar to us. So van Inwagen’s mistake is even stranger or more surprising when you look at it that way. What do I mean? I’ve talked about this more than once: what David Hume says, that you cannot derive the principle of causality or establish a causal relation between two events, between cause and effect, from observation. Observation teaches us nothing about causality. All I can see on the objective factual level is that there was event A and afterward there was event B. The claim that event A is the cause of event B, that it produced it, is a claim that is my interpretation of what I saw. What the eye sees—yes, observation as such does not show me that. I see a person kicking a ball and the ball flies off—yes, the example I always give. Or wood that is inside a fire and the wood burns. Okay, so I know that first the wood was in the fire and afterward it burned. How do I know that the fire is what burned the wood? Or I know that there was a kick and afterward the ball flew. How do I know that the kick caused or produced the flight of the ball? That I do not see in the observation. The observation… I can see that too. What do you mean always? Every time I saw it. But I cannot see the nexus of causation between A and B, the causal relation between event A and event B. That is an interpretation we give to what we see. It does not emerge from observation. So the view of the world, the deterministic view of the world as though everything were chains of necessary cause and effect, is really a product of our interpretation. It is not something we see in an observational, objective way. That’s with regard to causal processes. With regard to randomness, absence of cause and absence of reason, that is even less clear. We certainly don’t have that in our experience. With causality, we do grasp the events—a kick and then the ball flying—as a causal event; true, that doesn’t come out of the observation, but our logic or our reason tends to interpret it as events between which there is a causal relation. But an event without a cause—nobody even manages to conceive of such a thing. Certainly it’s not something we learned from our experience. When did we ever see an event without a cause? There is no such thing. Every event—we always, on the contrary, because we believe in the principle of causality, we assume for every event that at its basis there was a cause. And therefore one cannot say that we learn from our experience that there are occurrences without a cause. None of our experience shows us that, and to a large extent quantum theory, which according to the standard interpretations contains exactly this kind of event that is not produced deterministically by a cause, creates so much embarrassment and confusion and misunderstanding precisely because of this point. Because there is something there, or events there, that have no cause, we are not prepared to accept this thing, that there is an event without a cause. Meaning that both occurrences that have a cause—causal occurrences—and random occurrences are occurrences that we have no way of learning from observation. So out of the three kinds of behavior I described—the causal one, the random one, and free-will behavior—the causal and the random are things that are not drawn from experience; you’ve never encountered them. With regard to free choice, it seems to me that everyone, when he looks inward, understands in perhaps the most intimate and immediate way that I decide what I do. Schopenhauer once said that Kant divided between the thing-in-itself and the thing as it appears to us, the noumenon and the phenomenon. Meaning, the thing-in-itself is the way it is, and the thing as I grasp it, the way it is represented in my consciousness, is the phenomenon. And Kant basically argued that everything we know about the world, everything we say about the world, concerns its phenomenon, not its noumenon. Everything we say about it is about what we perceive, how we perceive it. Schopenhauer claims there is one exception. One place where we can see the thing itself and not only the way it appears to us, and that is when we look at ourselves. When a person looks at himself—not looking with his eyes, but contemplating with the eyes of the intellect, yes, contemplating himself, grasping himself, what is happening within him, how he makes decisions, and so on—there we have some access to the thing itself, not only to its external appearance to us, to our consciousness, because there we are looking from the inside and not from the outside. Now, our free choice we experience. When I look at you I don’t know whether you chose freely or not, but when I look into myself and I look at the way I myself make decisions, there I see in an immediate way that I make decisions freely. Not randomly and not causally, but purposively—that is, from some reason, in order to achieve something. I know the deliberations that take place within me before I do something, and therefore it seems to me that if there is anything among these three modes of behavior that we know in an immediate, personal, direct way, in itself—the thing itself, not only its appearance to us—it is free choice. And therefore to say that there is no such thing as free choice because really the two possibilities are either causality or randomness is not only incorrect because there is a third possibility, it is bizarre. Because the third possibility is the mode of behavior that we know in the most immediate way; it is the clearest to us that it exists. The other two modes of behavior are interpretations, if anything. One of them doesn’t seem possible to us at all, and the second is the product of interpretation. So to present those two possibilities as the whole picture and ignore the third is much more than an ordinary logical mistake where you missed another possibility. You missed the possibility that is most familiar to us and chose precisely the two that are not familiar to us, or at least not in an immediate way. So that’s regarding van Inwagen. I only used this to show that there are actually three forms of behavior. Now when I ask myself: when do we use statistics? Probability, statistics. In the simple sense, statistics describes random events. Right? Something that happens randomly—I say there are statistics, there is a distribution, it happens here, happens there, this can happen, that can happen, with this probability, with that probability. So I understand: there isn’t really a cause here; it’s something that happens just like that, and maybe I can say something about the probabilities. A fair coin or a die that I throw or something like that—we have some feeling that since there is nothing causal here, something that simply happens, I can describe it with probabilistic tools or statistical tools. But this conception is mistaken. And I talked about this right at the beginning of the series, because there I said, when I spoke about vagueness versus doubt, and I said fuzzy logic or vague logic as opposed to probability. I said that probability maybe deals with randomness, but fuzzy logic deals with vagueness, vagueness in reality. Now I’m looking at the same thing from a slightly different angle, but it’s the same distinction I made there. When I talk about tossing a coin or rolling a die, there is nothing random in these processes. If you look at them that way—not in the standard view, but try for a moment to think what’s going on there. I toss a coin or roll a die; then clearly there is some initial direction, initial velocity, environmental conditions of one sort or another. Once you know all those data, you can calculate on which face the die will land or on which side the coin will land. It is a deterministic result of the data. And therefore tossing a die or tossing a coin are not random processes at all. They are not accidental processes; they are completely deterministic processes. And if you think about it, you’ll see that every phenomenon you describe as a random phenomenon, and therefore use probabilistic or statistical tools for, is actually not random; it is deterministic. Every phenomenon you think of. There is not one phenomenon for which you use statistics that is truly random. Although statistics ostensibly describes a random occurrence. But randomness is a mathematical model. In the world we know nothing that is truly random. Every application we make of probability and statistics in the world speaks about events or occurrences that are not random. Most of them are deterministic, like the coin or the die or whatever. But there are in fact occurrences—and on second look you see it’s not few—that are actually occurrences of human behavior. We also use statistics with respect to that. So it turns out that among the three mechanisms I talked about before—the two of van Inwagen and free choice—statistics serves us, although it is defined to describe only random occurrence, in practice only with respect to the other two occurrences. That’s very strange. Meaning, not only does it not serve only with respect to randomness, it doesn’t serve at all with respect to randomness, because there is no randomness. It serves us only with respect to the other two occurrences. The only exception is quantum theory, and that’s why it is so strange. Quantum theory—again, according to the standard interpretations—there really is some dimension there that is genuinely random. It is not deterministic and it is not the result of free choice or anything; it is truly random. Therefore the application of probability and statistics in quantum theory is really the only application that truly applies to random things. But that is all in the microscopic world. In the macroscopic world, here in our world, the world we experience and have experience of, there is no quantum theory there. There we are really talking either about determinism or about human behavior, which at least can be the result of choice. And those are the two kinds of occurrences with respect to which we use statistics. Now why is this strange? Because when the occurrence is a causal, deterministic occurrence, then what room is there for probability? The result is one predefined and known result, and one probability. That’s it. That is what will happen. That is the meaning of a cause. When I kick a ball, there is no statistics. When I kick the ball, the ball will fly. And the kick will be the cause of the flight of the ball. Therefore our initial tendency to think that a deterministic occurrence is not a relevant candidate for statistical tools, for probabilistic tools. This is not the flesh into which statistics is supposed to sink its teeth. And yet, as we saw before, with tossing a coin, rolling a die, and so on, there we do use statistics. And why? Try to think about tossing a die or a coin—why indeed is there a different result each time? Newton’s laws are the same laws. The shape of the coin and the shape of the die are given. The coin and the die have a certain shape. The difference is in the question of what initial velocity I give them, with what force I push them, in what direction and in what manner. So in fact the statistics of a die or a coin falling speaks about me, not about the die or the coin. It speaks about the question of what velocity, at what angle, in what initial configuration I sent the die or the coin on its way. And here there are probabilities. Here it can be in this direction, it can be in that direction, and therefore each time it lands on a different side of the coin or a different face of the die. It’s not because of Newtonian mechanics. Newtonian mechanics—give me the initial conditions, and mechanics tells me what will happen in the end. Completely deterministic; there is no probability here or anything. The problem is that in the initial conditions there are many possibilities. I can set initial conditions like this, I can toss the coin here, I can toss it harder, weaker, in this direction, in another direction, to this height, another height, at a certain angle, and each such thing determines a different result. But once you have given me the angle and the force I gave the coin, we have determined the result. It’s deterministic; there are no probabilities. So the probabilities are really about how I send the coin on its way or the die on its way. Or in other words, probability describes what I do, not what will happen to the coin. Therefore the probabilities we talk about when we talk about a coin or a die are really probabilities connected to human behavior. To the question of what I will do with the die or the coin. True, this is human behavior that is not exactly the result of a decision, because I decide to send the coin, but I cannot decide on the angle and the force while knowing what result will come out. I have no way of knowing. I cannot know what will happen when I send the coin and the die; the calculation is very complicated. So I do not decide the result, but I do decide the angle and the force with which I toss the coin and the die. And in that sense, this is statistics about human behavior. So even when we talk about statistics with respect to deterministic events, many times what is really hidden behind this is statistics that speaks about human behavior. So surprisingly, we would have expected statistics to deal only with random events, and we would have expected that with respect to deterministic events, statistics would not be relevant because there is one result and its probability is one. If you give me the data, I’ll tell you what the result will be; so in deterministic behavior statistics is not relevant. And with respect to free-choice behavior or human behavior, there apparently statistics does not belong there, but I understand that it’s not deterministic; there is something here that maybe one can try to think about statistically. It turns out that the third is the best candidate for statistics. A process that is truly random in the world—okay. So in effect, although at first glance it doesn’t seem that way, statistics definitely does operate with respect to human behavior, which is surprising, because human behavior is not accidental, it’s not random. I make decisions, I deliberate and make decisions. Why should statistics be a relevant tool at all for dealing with this kind of occurrence? The occurrence is not random; I’m not drawing lots when I make decisions, I deliberate and decide what I want to do. In a certain sense this resembles deterministic behavior. Why should statistics be relevant at all with respect to this? So here I want to go in a bit more, in order to understand how this nevertheless works. I want to look at this through a well-known Maimonides in the Laws of Repentance. Let’s see, Laws of Repentance chapter 6, Jewish law 5. I’ll remind you that chapter 5, Jewish law 5 is the famous question of foreknowledge and choice, but here it’s one chapter later, chapter 6, Jewish law 5. “And what is this that David said: ‘Good and upright is the Lord; therefore He instructs sinners in the way; He guides the humble…’ This means that He sent them prophets who inform them of the ways of the Lord and bring them back in repentance, and furthermore He gave them the power to learn and understand, for this quality exists in every person—that whenever he is drawn in the ways of wisdom and righteousness, he desires them and pursues them. And this is what our sages said: ‘One who comes to purify himself is assisted,’ meaning he will find himself helped in the matter. But is it not written in the Torah: ‘And they shall enslave them and afflict them’? Behold, He decreed upon the Egyptians to do evil.” Yes, the Holy One, blessed be He, in the Covenant Between the Pieces decreed in advance that the Egyptians had to do evil, to enslave the Jewish people. “And it is written: ‘And this people will rise up and stray after the foreign gods of the land’—did He then decree upon Israel to worship stars and constellations? And why then does He exact punishment from them?” Right, he said above that in the way a person wishes to go, he is led; yes, that basically the Holy One, blessed be He, helps us do what we decided to do. So Maimonides asks: if so, and the proof is that the Holy One, blessed be He, sometimes even gives us prophecy of what we will decide to do—He tells us in advance what will happen, yes, like “this people will rise up and stray after the foreign gods of the land”—then the Holy One, blessed be He, said in advance that we will worship idols, the Jewish people. Or the Holy One, blessed be He, said in advance that the Egyptians would enslave the Jewish people: “and they shall enslave them and afflict them four hundred years.” So if the Holy One, blessed be He, says this in advance, and in fact He is the one who helps people do what they do, then why does He exact punishment from them? What punishment is due to the Jewish people for idolatry, or to the Egyptians for enslaving Israel? Since… so he says this, Maimonides says, this is the answer, this is the question: “Did He then decree upon Israel to worship stars and constellations, and why then does He exact punishment from them? Because He did not decree upon any particular known individual that he would be the one who would stray; rather, each and every one of those who strayed to worship stars and constellations—had he not wished to worship, he would not have worshiped. And the Creator merely informed them of the customary way of the world.” What does that mean? Maimonides says: although the Holy One, blessed be He, said in advance that the Jewish people would worship idols, for each person in the Jewish people it was not decreed upon him that he would worship idols; that is his own decision, free choice. Each person in the Jewish people has free choice. “And the Creator merely informed them of the customary way of the world.” So what does it mean that the Holy One, blessed be He, said in advance that the Jewish people would worship idols? “The Creator merely informed them of the customary way of the world.” Meaning, that’s what will happen in the ordinary course, but each individual has free choice. To what is this comparable? To someone who says: among this people there will be righteous and wicked people. Yes, if the Holy One, blessed be He, had said: in this people there are righteous and wicked. Now the wicked person comes and says: the fact that I chose to be wicked is not my fault—what do you want from me? The Holy One, blessed be He, said that in this people there would be righteous and wicked. Meaning, “the wicked person will not say, because it was already decreed upon him that he would be wicked, because God informed Moses that there would be wicked people in Israel,” as in the verse “the poor will never cease from the land.” And likewise the Egyptians: each and every one of those Egyptians who harmed Israel—had he not wished to harm them, the choice was in his hands. No Egyptian was obligated to enslave the Jewish people; he has free choice, for the Holy One, blessed be He, did not decree upon any known individual. A particular individual cannot say: the Holy One, blessed be He, decreed upon me to enslave Israel. Rather, He informed them that in the end his descendants would be enslaved in a land not theirs. And we have already said that it is not within human power to know how the Holy One, blessed be He, knows things that are to occur in the future,” which refers to what he said in the previous chapter, in chapter 5. Basically what Maimonides is saying here is that even if the Holy One, blessed be He, gives us a prediction, yes, a forecast, of what some group or some nation will do in the future, that does not provide any excuse to anyone from that nation who chose to do what he did, because every individual in that nation has free choice. But still, despite the fact that every individual has free choice, the Holy One, blessed be He, can say in advance what will in fact happen here. How can that be? So apparently Maimonides explains this; he refers us back to what he said in the previous chapter, that the knowledge of the Holy One, blessed be He, does not compel free choice, and we have no power to know this matter, how the Holy One, blessed be He, knows what will happen. So on this the Raavad comments, the gloss of the Raavad, yes? “But is it not written in the Torah, ‘and they shall enslave them and afflict them,’ etc.” Abraham said: “These are lengthy words without flavor,” they contain no seasoning, no sense, words without sense. “And by my life I almost say that they are childish words. The Creator will say to those who stray: why did you stray? And I did not mention you by name”—I did not mention your name when I said that the Egyptians would enslave the Jewish people—“so why did you stray?” Yes, the Holy One, blessed be He, comes with claims against one of the Egyptians, “and I did not mention you by name so that you could say that I decreed it upon you.” The sinners will say to Him: “And upon whom did Your decree fall? Upon those who did not sin? Behold, Your decree was not fulfilled.” I don’t understand—you decreed that all of us, that we would enslave the Jewish people or that we would stray after idolatry, and then You come to me with claims because I worshiped idols? And You tell me: listen, I didn’t determine that you would worship idols. So I’ll ask Him: tell me, then whom did You mean? Those who did not stray? Those who did not stray didn’t stray at all, so what You said was not true about them. Obviously You were speaking about those who did, which is me. So what are You telling me—that You did not determine or produce this idolatry that I committed? Or this enslavement by which that Egyptian enslaved the Jewish people? What does Maimonides want? What kind of childish, senseless talk is this? What kind of argument is this? If the Holy One, blessed be He, determined it, then He can’t say: I didn’t determine your name, I didn’t say it would be your name. Okay, so what? So You meant someone else? Therefore the Raavad says: what Maimonides says has no seasoning; it makes no sense. And this is what he said: “But regarding ‘and this people will rise up and stray,’ we have already said that in this matter the Creator’s knowledge is not a decree. All the more so here, where even Moses said, ‘you will surely act corruptly while I am still alive with you, and all the more after my death’; all the more so the Creator could say this without decreeing it.” What does the Raavad say? He says: I don’t understand at all what is difficult for Maimonides. Maimonides asks: what do you want from the Egyptians if the Holy One, blessed be He, decreed in advance that they would enslave Israel? The Raavad says: what do you want, Maimonides? In the previous chapter you already answered that. That the fact that the Holy One, blessed be He, knows what will happen is not because He dictates it. I have free choice, and still the Holy One, blessed be He, knows in advance what I will do. Therefore it’s not because He did or did not mention me by name. The Raavad says: even if Maimonides had said—even if the Holy One, blessed be He, had given in advance a list by name of the Egyptians who would enslave the Jewish people, still one could come to them with claims: why did you do it? And likewise to the Jews who worshiped idols. One could still come to them with claims: why did you do it? Why? Because the fact that the Holy One, blessed be He, said it in advance is because He knows what will happen, but that doesn’t mean that He produced what happened; He only knows what will happen, but that doesn’t mean the blame is not on the one who chose. The Holy One, blessed be He, knows in advance what I chose—that is basically the Raavad’s claim, consistent with his view in the previous chapter as well. And therefore he says: I don’t understand at all—even before I get to Maimonides’ answer, which is a childish answer—I don’t understand what question he is even troubled by. It is the same question he answered in the previous chapter: despite the fact that the Holy One, blessed be He, knows everything in advance, we still have free choice whether to do it or not. So why do you need to get into the fact that this is some collective statement about all the Egyptians, that the Holy One, blessed be He, did not specify the name of each Egyptian case who would or would not do it? That’s not relevant. Even if He had specified the name of this case and that Egyptian, one could still come to him with claims. Because prior knowledge does not negate his free choice, and he chose freely, and so punishment should be exacted from him and he should be held accountable for his choices. “And the matter of the Egyptians is not a question for two reasons.” Since he says: why did the Egyptians enslave the Jewish people—after all, the Holy One, blessed be He, said in advance that they would do it. “The first, because it is known that the Creator does not exact punishment from an evil person except through one more evil than he, and after He exacts punishment from this one, He returns and exacts punishment from the one more evil than he for his own wickedness. And so it says: ‘Woe to Assyria, the rod of My anger’… ‘when you finish destroying, you shall be destroyed’—meaning, because of your wickedness and the greatness of your heart and your arrogance against Me, etc.” What is he saying? He says the Egyptians were basically like the case where the Holy One, blessed be He, hardened Pharaoh’s heart. So the commentators say that Pharaoh deserved punishment, and therefore the Holy One, blessed be He, hardened his heart, took away his choice, and then punished him for what he did, even though what he did was the result of the hardening of the heart that the Holy One, blessed be He, imposed on him. Yes, but the hardening of his heart was because of previous sins that made him deserving of it, and so in the end he deserves the punishment. And that is what he says: “The Egyptians too were wicked and deserving of these blows. Had they listened to Moses at first and sent out Israel, they would not have been smitten nor drowned in the sea. But Pharaoh’s willful sin and his contempt for the Creator, blessed be He, before he sent them out—that caused it.” Yes, so that is basically previous sins. And that is the first explanation; he said there are two explanations. “And the second, because the Creator said ‘and they shall afflict them,’ and they worked them with crushing labor and killed some of them and drowned some of them, as it says, ‘I was only a little angry, but they helped make it worse’; therefore they became liable.” The Holy One, blessed be He, said: you will enslave Israel; He did not tell them to work them with crushing labor and kill them and drown them in the sea. You added beyond the decree of the Holy One, blessed be He, and therefore claims are brought against you. These are the Raavad’s answers. Those answers, of course, do not hold water in any way, because the first answer—yes, it reminds me of the Gemara in tractate Makkot 10b. The Gemara says there: what is the case of accidental manslaughter? How does this matter of killing accidentally occur? The Gemara says: Reuven was liable to death and Shimon was liable to exile because of previous sins. What does the Holy One, blessed be He, do? He brings them to one inn: Reuven below, Shimon above with an axe on the roof, and then the axe accidentally falls from Shimon and kills Reuven. Reuven, who was liable to death, got his death, and Shimon, who was liable to exile, now becomes an accidental killer and receives exile. That’s how the Gemara describes it. The great difficulty regarding this Gemara is how the whole thing started. How did Reuven or Shimon—sorry—how did Shimon become liable to exile beforehand? Now he is already liable to exile, so the Holy One, blessed be He, arranges the matter. But how did he become liable to exile then? Because he killed accidentally? How did that earlier accidental killing happen? Also because there was an even earlier accidental killing, so the Holy One, blessed be He, brought them to one inn, and so on and so on. How does it begin? It’s turtles all the way down. After all, at some point there must be some act that is not the result of the deed of the Holy One, blessed be He, and because of which I truly deserve punishment. From there onward the Holy One, blessed be He, can arrange matters: merit is brought about through the meritorious and liability through the liable. But first I need to be liable, and only then can one begin to speak this way. How does this chain begin? This is not… something here is not logical. You can’t tell me that every accidental killer is because someone was really liable to exile already beforehand. Fine—then I’ll ask you about the earlier one: how was he liable to exile? How did that happen? Because he killed accidentally even earlier? So every accidental killer committed infinitely many accidental killings. Is there no accidental killer who killed accidentally only once? These are strange explanations. These explanations basically assume that there are actions that a person does and the Holy One, blessed be He, does not cause them. Only sometimes there may be a situation where the Holy One, blessed be He, causes the person to perform some action, and still it is counted against him because the very fact that the Holy One, blessed be He, causes the action through him is because he had a previous sin. And in fact the punishment he deserves is punishment for the previous sin he had, not for what he did here. What he did here is the result of the fact that the Holy One, blessed be He, caused it. But the punishment he deserves is for the previous sin he committed. Let’s say that’s possible—I have no idea whether it’s correct, why it’s correct, or who told the sages that it’s really true. But even if we assume it’s true, clearly it does not explain all the actions that happen in this world. Because if everything were the result of the work of the hands of the Holy One, blessed be He, then these explanations don’t even get started. At some point a person has to become wicked on his own, so that afterward his choice can be taken away and one can play with him so he does something evil and then gets hit, because he was wicked to begin with anyway. But the first wickedness must be the result of an act that he himself did, not that the Holy One, blessed be He, caused it. Therefore one cannot escape the fact that clearly a person can choose freely and it will not be the work of the hands of the Holy One, blessed be He. It may be that there are circumstances or certain actions where, although the person did it, in fact the Holy One, blessed be He, caused it. He wanted to cause it because that person was wicked; He wanted to bring about the matter through him in order to punish him in that way. Fine—like with Pharaoh, like with the Egyptians, like with anything. But all of that begins from the fact that you were wicked. And being wicked is because you decided to do something, not because the Holy One, blessed be He, decided to do it through you. So one cannot escape this point. Therefore what the Raavad says here cannot be right: that the reason claims are brought against the Egyptians is because they were wicked beforehand and the Holy One, blessed be He, caused it. So what will you say about the earlier wickedness? And the second explanation he says there—that the Egyptians did more than the Holy One, blessed be He, foretold—that could in principle be correct, but then you are basically assuming that there are some things that are not in the hands of the Holy One, blessed be He, and some things that are. The assumption of the question is that all things are in the hands of the Holy One, blessed be He. And if you tell me that there are things that are not in the hands of the Holy One, blessed be He, but that human beings do them, then you are basically saying: okay, so there are things that the Holy One, blessed be He, does, and as for those they are outside the game, and punishments come only for what the person himself did. So the question never gets off the ground in the first place; there is no confrontation here between foreknowledge and choice, because regarding that there is no foreknowledge and the Holy One, blessed be He, does not cause it and nothing of the sort. And therefore the person is punished and that’s all. The Raavad tries to explain how it is possible that despite the fact there is foreknowledge, one can still come with claims against the person. But there is something here that cannot work. On the other hand, apparently his objection to Maimonides is correct. After all, what is the difficulty that troubles Maimonides? The difficulty is that the Holy One, blessed be He, knew it in advance—so what? In chapter 5, in the previous chapter, Maimonides already told us that even if the Holy One, blessed be He, knows in advance, that does not mean the act was not done out of my free choice. And if it was done out of my free choice, then I deserve punishment for it. So what troubles Maimonides in the fact that the Holy One, blessed be He, said, “and they shall enslave them and afflict them four hundred years,” and also, “and also the nation that they will serve I will judge”? For what do You judge them? For what do You punish them? After all, You are the One who created it. That is not true—I only foretold that it would happen; I did not create it, and therefore I can punish them; they did it of their own free choice. I think what Maimonides wants to say here—and here I come to the point for which I need this whole move.

[Speaker C] What Maimonides—the Rabbi, Rabbi, Rabbi? Yes. Rabbi, if the Egyptians had some representative whom they chose, and he says, I represent everyone, then you say—Maimonides says—personally each one can choose, but in advance You knew statistically or whatever that this is what would happen, so again, what claim are You making against them? That’s the difficulty.

[Rabbi Michael Abraham] That is exactly the Raavad’s objection. That’s why I said: the Raavad’s objection to Maimonides is apparently a good objection. You said: what does Maimonides want? The Raavad’s answers are not answers, but his objection to Maimonides is a good objection. So I want to argue that what Maimonides really wants to say is that we can speak—or the Holy One, blessed be He, can say—look, collectively the Egyptians will enslave the Jewish people. In principle I know that as a phenomenon, that is what will happen. Every Egyptian individually has free choice, but statistically I’m telling you that a certain percentage of the Egyptians will enslave the Jewish people. And that is what Maimonides says: this is not beyond the question of foreknowledge and choice. Here, even if the Holy One, blessed be He, dictates the result—not only knows it in advance, but dictates the result—it is still possible to come with claims against each person who decided to do it. Because the dictation was not about a specific individual; rather, it was a statistical dictation. In effect, I said what the collective would do; I did not say who within the collective would do it. And therefore every person who decided to do it, that was the result of his free choice, and one can come with claims against him. That is basically Maimonides’ claim.

[Speaker C] So again, if the representative of the Egyptians comes and says, you as a representative of everyone—personally I… then as a nation we don’t deserve

[Rabbi Michael Abraham] What?

[Speaker C] what you’re bringing upon us?

[Rabbi Michael Abraham] I’ll formulate it differently. I think you mean the same question, but I’ll put it differently. Basically, we still haven’t solved the problem. I’ll formulate the Raavad’s objection in another way; maybe that’s also what you mean. Suppose there are a hundred Egyptians. Now you tell me: each one has free choice. But I tell you that ten of the Egyptians will enslave the Jewish people. And each one has free choice. Now if each one has free choice, then in principle ninety-nine Egyptians could choose not to enslave the Jewish people. Each one has free choice and is also independent of the others—that’s what free choice means. Now the hundredth Egyptian comes along. The other ninety-nine decided not to enslave them. Now the hundredth Egyptian—does he have the option not to enslave the Jewish people? He doesn’t. Because the Holy One, blessed be He, already knew in advance, already said in advance, that there would be Egyptians who would enslave the Jewish people. So if the other ninety-nine—and that can happen, because there is free choice—chose the good, then the hundredth is basically compelled to choose evil. So what do you want from him? Now of course this is just taking the point to an extreme, but it’s true even about ten Egyptians. If the Holy One, blessed be He, said that ten Egyptians would enslave the Jewish people, and ninety Egyptians already chose the good, then those ten have no choice; they must enslave them, because the Holy One, blessed be He, determined it—indeed dictated it, not just knew it—that ten would enslave the Jewish people. So this means that the Raavad’s objection, in this formulation, still exists even if I make Maimonides’ claim, which is a collective claim: that the Holy One, blessed be He, did not decree it about a person with a particular name, a particular identified individual, but rather about the Egyptian collective, or about the Jewish collective—that “this people will rise up and go astray.” Okay? By the way, “this people will rise up and go astray” is pretty clearly not something dictated by the Holy One, blessed be He; it’s only foreknowledge. But with the Egyptians, it could be that the Holy One, blessed be He, also brought about the enslavement—He wanted there to be enslavement there, that was His plan, and therefore He caused the Egyptians to enslave the Jewish people. So there’s some difference between the two examples, but I’m not going into that difference right now. What I want to argue—and this brings me to the point—is that the Holy One, blessed be He, could have acted in such a way.

Suppose there are a hundred Egyptians—not a hundred, a million Egyptians, okay? Now the Holy One, blessed be He— in principle every person has a choice between good and evil, and let’s assume for the sake of a simple model that for each person the weights of good and evil are equal. Let’s assume that. It’s not true, but let’s assume for the sake of discussion: fifty-fifty. There’s a fifty percent chance he’ll do good, a fifty percent chance he’ll do evil, okay? So if I have a million Egyptians, then I assume that fifty percent of the Egyptians will do evil and fifty percent will do good. If I assume the Egyptians have free choice, then—or prior to the exercise of free choice—fifty percent will do good, fifty percent will do evil. Which fifty percent will they be? There’s no way to know. Any given Egyptian could end up on the side of good or the side of evil. But I do know probabilistically, by the law of large numbers, that fifty percent of the Egyptians will do evil and fifty percent will do good, even though each individual Egyptian has a choice and can decide either way, and let’s say he makes that choice like a coin toss, fifty-fifty. By the law of large numbers, I know that fifty percent of the Egyptians will be on the evil side, even though for each one the result is like a coin toss. In principle, the coin tosses are free. Theoretically, it could happen that all the Egyptians toss the coin and all of them get heads. In principle such a result is possible—very rare, but possible. But on average, especially when the numbers are large, it will come out fifty percent heads, fifty percent tails. In other words, when we’re dealing with large numbers, I can say in advance that there will be Egyptians who enslave the Jewish people, even though each one individually makes a free decision between good and evil, let’s say with a fifty-fifty probability.

But the probability of doing evil usually isn’t fifty percent; people generally have a tendency to do good, even in terms of our conscious decision-making, not just our impulses. We want to do good, even if we have an impulse to do evil. So in a normative population, the tendencies—let’s say the probability of doing good versus doing evil—is ninety-eight to two. Not fifty-fifty. Ninety-eight to two, for the sake of discussion. And still, two percent of them will do evil, ninety-eight percent will do good. The Holy One, blessed be He, can of course change the distribution. He can say: the distribution is not two percent versus ninety-eight, but rather I’ll build your spiritual environment, your psychological environment, in such a way that you have a weight pulling you in the direction of evil. And now the distribution will no longer be two versus ninety-eight, but forty versus sixty. Still a minority—the majority, sixty percent, doing good; forty percent, doing evil. What happens by the law of large numbers? By the law of large numbers, forty percent of the Egyptians will enslave the Jewish people, or forty percent of the Israelites will worship idols—whatever the numbers may be in each case. Notice: every one of these people has free choice between the two possibilities under a certain distribution, and he could have chosen the good, he could have chosen the evil. But still, with large numbers, if a sufficiently large number of people is involved, I can tell you that a certain percentage will choose evil. I can tell you that in advance, even though every individual has free choice. I’ll tell you more than that: it’s not despite the fact that each person has free choice; it’s because each person has free choice.

Let’s take an example. Look at a coin toss. In a coin toss, when I toss one coin, I have a fifty percent chance of getting heads and a fifty percent chance of tails. What happens if I toss ten coins? Then I expect some tosses to land heads and some to land tails. On average it should be five and five; in practice it almost never comes out exactly five and five—it’ll be three-seven, six-four, two-eight, I don’t know, something like that. Some tosses will come out this way and some that way. What happens if I toss a million coins? If I toss a million coins, the uncertainty narrows dramatically; it will be more or less half a million heads and half a million tails. That’s the law of large numbers. Now notice the strange and surprising thing here. The law of large numbers is true only when the tosses are independent. If I have a million coins and I toss each one, and each toss is independent of all the others, then precisely in that case I can tell you in advance what the result will be: fifty percent heads, fifty percent tails. If there is influence among the tosses—some link, some dependence among them—then you can’t apply the law of large numbers. The law of large numbers doesn’t work.

Now notice how strange the result is that I just described. Precisely in the place where I can’t say anything about the individual toss, I can say exactly what will happen in a large number of tosses. If I can say something about the individual toss, then I can’t say anything about a great many tosses—or at least it won’t proceed statistically according to the law of large numbers. So that’s a bit odd. And precisely because I can’t say anything about the individual toss—that’s the condition—if that holds, then about large numbers, about many tosses, I can tell you exactly what will happen. How can that be? After all, if each toss can come out heads or tails freely, what prevents all of them from coming out heads? Or seventy percent heads instead of fifty? Let me ask the Raavad’s question now about a coin toss, okay? I made a million tosses. Nine hundred ninety-nine thousand nine hundred ninety-nine tosses have already come out heads. The next toss is independent, right? It knows nothing about what happened until now; it’s independent of the previous tosses. So it can come out heads and it can come out tails. You understand that there’s a fifty percent chance it too will come out heads, just like all the previous ones, and then everything will come out heads. In other words, the fact that the last toss doesn’t know what happened before it, that the third toss doesn’t know what happened in the first two tosses, and so on—and precisely because each one doesn’t know what happened before, they arrange themselves in a way that appears, seemingly, to have been ordered in advance, so that I can say beforehand what will happen there. Precisely because they don’t know about one another. It’s very strange when you think about it, even though intuitively it’s obvious to us that it’s true.

We also understand—and try for a moment to think about this phenomenon and you’ll see how strange it is. If I roll a die millions of times, one sixth of the time it will land on one, on two, on three—each exactly one sixth if I roll it enough times, yes, by the law of large numbers. It will come out exactly one sixth. Now none of the rolls knows anything about the others, so how do they arrange themselves in such a way that the outcomes get divided up among them into one sixth of the time for one, one sixth for two, one sixth for three, and so on? They don’t know about one another. So I’m saying not only “how can this be,” but rather it is precisely when they don’t know about one another that it organizes itself this way. That’s the rule. Only then does the law of large numbers exist. The law of large numbers exists only for a large number of trials, each of which is independent of the others. In such a case, the a priori distribution is realized in practice. The a priori distribution in a fair coin is fifty-fifty. In practice, when you toss the coin, if you toss it many times, the outcome will realize that a priori distribution—fifty-fifty. That’s the law of large numbers. But that happens only if each toss by itself is independent of all the others; it doesn’t know about them, doesn’t depend on them, and isn’t coordinating with them. If they were all coordinating together, then I could understand their saying: okay, first toss, third toss, tenth toss, twenty-fourth toss and so on—you land on one; these tosses land on two; these tosses land on three. If they organize together, I can understand how one sixth of the tosses land on each number, because then it’s somehow organized, there’s a connection among them. But why does this happen precisely when there is no connection, when they are not coordinating with one another? Precisely then. That’s the law of large numbers, and when you think about it this way it’s very hard to understand—very hard to understand—although it seems totally obvious and intuitive to us. When you think about it in this form, it’s very hard to understand.

What I want to claim is that the same thing exists with respect to human behavior. When the Holy One, blessed be He, prophesies—suppose He even prophesied quantitatively, saying forty percent of the Egyptians will enslave the Jewish people. Not all of them were there—forty percent, say, for the sake of discussion, will enslave the Jewish people. How can He do that, asks the Raavad about Maimonides, if every single Egyptian has free choice? The answer is that every single Egyptian really does have free choice, and precisely because of that it’s possible to know in advance what the overall distribution will be. Because if the Holy One, blessed be He, set the weights that incline each Egyptian toward evil or toward good, say forty-sixty, then each Egyptian decides freely. But out of a million Egyptians, four hundred thousand will enslave the Jewish people. Precisely because each person’s choice is free—not despite it, because of it. It’s really strange. And the Raavad’s objection was: wait a second, there’s free choice here—what’s going on? So I would have expected Maimonides to answer: no, despite the fact that there is free choice, it still somehow organizes statistically. But the answer is stronger: because each person has free choice, it organizes statistically according to the law of large numbers. Not just despite it, but because of it.

In other words, when we deal with large populations, I can predict for you what that population will do even though every individual in the population has free choice. If I had to address or predict what this or that individual within the group would do, I have no way of predicting that. I can’t tell you what he will do. I can tell you that forty percent will do this and sixty percent will do that. What will he actually do? Whatever he decides. But if there is a large group of people, I can tell you on the macroscopic level that forty percent of them will do this and sixty percent will do that. I can tell you what will happen, precisely because each person has free choice—not despite it, because of it.

Now notice: there’s a certain leap I made here, because the choice whether to do evil or do good is not a coin toss. It’s not a random event. That’s what I spoke about at the beginning of the lecture. It’s an event that is the result of a person’s choice. It turns out that even though we are dealing with events that are the product of choice, statistics still has something to say. It’s like a lottery. Choice only says—let me put it this way—suppose every person’s impulse toward evil has a strength of ten percent, say, only in a certain situation. On average, in such a situation there is a force of ten percent pulling people toward evil and ninety percent pulling them toward doing good. Now besides the struggle between those forces, there is also a person’s free choice. Human beings tend to choose the good even though it may be hard to do good, so I expect that in practice not ninety percent of people will do good but ninety-eight percent will do good, because they are also choosing to do good. So let’s also put that inclination to do good, that choice, into the calculation. And now I say: ninety-eight percent that each one will do good. Now a specific person standing here—I don’t know what he will do. Maybe he is among the two percent who do evil. But if there are a million people here, I can already tell you in advance: nine hundred eighty thousand of them will do good, twenty thousand of them will do evil. Meaning, even when there is free choice, I can incorporate that into statistics if I’m talking about large populations.

And of course this is also true of things not connected to free choice, like a coin toss. Although as we saw, even a coin toss is actually the product of human decisions. But in short, all the applications we know of probability and statistics suffer from the same paradox. Basically, we give a forecast for large groups, and that forecast is reliable only where every individual in the group, or every case among the set of cases, occurs through free choice or through a completely random lottery independently of all the other trials. Then—and only then—we can predict what will happen in the end. So contrary to the usual view, that free choice prevents prediction—you can’t know in advance what will happen if a person has free choice—in large groups free choice not only does not prevent prediction, it is what makes it possible. Without free choice I couldn’t predict. It’s strange. Free choice works in a certain sense like a lottery, even though it is a different mechanism, as I said before. It turns out that free choice also works like a lottery. By the way, non-free choice also works like a lottery. For example, the choice of with what force and in what direction to toss the coin. That’s not a choice I make consciously—I’m not deciding to put it at a thirty-degree angle with such-and-such force. No, I just do this. It’s my decision what to do, but I don’t decide the parameters; I simply do something. So it’s a human decision, and that decision is handled with statistical tools. The fact is that with a die or a coin, if it’s a fair die or a fair coin, we assume the distribution is fifty-fifty or one-sixth each, even though this is an action of human beings deciding how to do it. It turns out that human actions—both actions by choice and technical actions like I said before—can basically be described using statistical tools. And not only can they be; only if the actions are done in this way are the statistical tools applicable to them. And then the Raavad is not right in his objection to Maimonides.

Because Maimonides is basically saying this: the Holy One, blessed be He, does not—in chapter 5 Maimonides says that what the Holy One, blessed be He, knows does not dictate the choice. Never mind that right now; I have a different thesis about that Maimonides, but I’m leaving it aside for now. In chapter 6 Maimonides is not speaking about situations that the Holy One, blessed be He, merely knows in advance. Maimonides is also speaking about situations in which the Holy One, blessed be He, dictates what will happen. Not that He knows and then you do what you do—no, He dictates what will happen to you. There Maimonides indeed asks: so how can He punish them? It’s not just that I knew in advance what would happen—that’s chapter 5; I explained that. If I know, there is still free choice. But in chapter 6 I’m speaking about situations where I dictated the result, not just knew the result. The Holy One, blessed be He—yes, that’s me. So how can you punish them here? Maimonides says: when the Holy One, blessed be He, dictated to the Egyptians to enslave the Jewish people, He did not dictate to any specific Egyptian to enslave the Jewish people. What did He do? He changed the weights of their choice. The fork in the road at which every Egyptian stood was no longer balanced. There was some artificial tilt that the Holy One, blessed be He, created toward the evil choice and the enslavement of the Jewish people. And therefore the Holy One, blessed be He, knows in advance that forty percent or sixty percent or whatever percentage of the Egyptians will enslave the Jewish people, even though He did not dictate it individually; He only tilted the weights. Once you tilt the weights, you’ve basically determined the result in large numbers, you’ve influenced the result—and that is not merely despite the fact that each person has free choice, but because each person has free choice.

As an analogy, think about my telling you: take this coin. And I tell you, you think this coin will land fifty percent heads and fifty percent tails. You’re about to toss it a million times, and you assume it will be fifty percent heads and fifty percent tails. I tell you in advance: it will be—but sixty percent heads and forty percent tails. How can I not only say it in advance but also determine that this will be the result? I can tamper with the coin, turn it into something unfair, so that one side weighs more than the other, and therefore it will tend to land more often on the heavier side. The heavier the heavy side is relative to the light side, the more that determines the weights—whether it will be forty-sixty, thirty-seventy, or something like that. So manipulating the coin essentially determines the result—not the result of an individual toss; an individual toss can still come out heads or tails no matter what I do to the coin. But if you toss it a million times, then if I control the coin I can tell you what the result will be in large numbers, even though each toss is free. But once I set the weights in a certain way, I’ve basically fixed the result.

And that’s what Maimonides says: each Egyptian has free choice, but the Holy One, blessed be He, changed the relative weight of the two sides of the choice—whether to enslave the Jewish people or not to enslave the Jewish people—and made it harder for the Egyptians to choose the good, meaning He caused them to incline more toward evil. Still not deterministic; each one has free choice. But the weights are now arranged differently. And if that is the situation, then the Holy One, blessed be He, can know in advance by the law of large numbers that forty percent of the Egyptians will enslave the Jewish people.

[Speaker B] How did He arrange those weights? On the inner level? I mean, an inner hardening of the heart like with Pharaoh? Or externally, in the sense that the external conditions suddenly changed? Because the external conditions actually seemed to say the opposite: the more you continue, the harder you’ll get hit, so maybe they should have gone in the other direction.

[Rabbi Michael Abraham] It doesn’t matter how He did it. It could be internal, it could be external. I have no idea what happened there. I’m only proposing a model for how it could be that the Holy One, blessed be He, predicts in advance and still has claims against people. Not only predicts, but dictates.

[Speaker B] And is that Pharaoh’s hardening of the heart here? And is that taking away the freedom of free choice if He hardened his heart?

[Rabbi Michael Abraham] No! Free choice does not mean that it’s fifty-fifty. Free choice means that the matter is in your hands. But whether it’s hard or easy to do, that depends on circumstances. Let’s say someone really angers me, so I have an inclination to respond violently because he provoked me. Does that mean I have no free choice? That I can’t be judged for what I did? Of course I can. It was harder for me to overcome it and restrain myself, but I’m still expected to restrain myself. Now if you put a thousand people or a million people in such a situation—without provocation almost nobody will be violent; maybe, I don’t know, one percent will be violent. With provocation, maybe, I don’t know, seventy percent will be violent. With very, very extreme provocation, say seventy percent will be violent. In the second case, if a person now comes before a judge, will I punish him or not? Of course I will. Even though it was hard for him to overcome it. Hard, yes—but I still expect you to overcome it. You know it’s wrong to do that, so overcome it. Hard? Hard. That’s the meaning of free choice. Free choice does not mean that there are no weights influencing me or inclining me. Free choice means that even though there are different weights pulling in different directions, in the end I can decide what I do. If that is the case, then I had free choice. Free choice does not mean all sides are equal. By the way, if all sides had to be equal, then nobody would ever have free choice, because no dilemma is ever exactly fifty-fifty. So it’s a mistake to think about free choice that way. Meaning: you can predict.

[Speaker C] How does the Rabbi explain Maimonides, who says that a person can be righteous like Moses our teacher or wicked like Jeroboam, and no one draws him to either side? As if it’s fifty-fifty, completely free, and he chooses.

[Rabbi Michael Abraham] “No one draws him to either side” means that everything is in his hands. But it doesn’t mean it will be exactly as easy for him as it was for Moses our teacher or as it was for Jeroboam. That’s what “no one draws him to either side” means: there is nothing that compels him deterministically toward either side. But of course there are different weights. What do you mean? Isn’t it obvious that there are people for whom it’s harder to rise to high levels and people for whom it’s easier? Of course there are. And still it is true to say that no one draws you—doesn’t draw you in the sense that it does not dictate. One of the great mistakes—and I’ll talk about this next time, I see I won’t have time to get to it now—one of the great mistakes is this identification of free choice with absolute freedom, with the absence of weights. No. Free choice does not mean that all directions are equal for me, but rather that all directions are in principle open to me, meaning I can go toward them. How hard will it be? There may be directions that are hard and directions that are less hard. Still, if I can do it, that is free choice. And to say that different weights or different constraints affect me—that is certainly true. To say that the different constraints dictate the result—that is not true, if you are not a determinist. The constraints influence me, but they do not dictate the result. In large numbers the constraints almost dictate the result. That’s the law of large numbers.

Even though on the theoretical level it could happen that all the Egyptians choose good. The chance of that is very, very small. But in principle it could happen, because each one has free choice. There’s some sort of Gaussian in the law of large numbers, where the center of the Gaussian says that the Egyptians will choose according to the a priori distribution. That’s what will happen. But theoretically it could happen that all the Egyptians are suddenly seized by a spirit of righteousness and they all decide to choose good—or choose evil. They don’t have to; there is free choice. But in practice it won’t happen. You know, in quantum theory, for example, we know that a soccer ball that you kick into a wall can in principle pass through to the other side according to quantum theory. For a microscopic particle, the probability of that is definitely real. For a very large object, a ball composed of many, many small particles, that probability is practically nonexistent, it goes to zero. And therefore it doesn’t happen in the everyday world that we experience. That’s the law of large numbers. And the same thing applies to prediction regarding the Egyptians or regarding the Jewish people who worshiped idols. About each individual I can’t predict anything. But collectively I can say what will happen—and notice, there is a small chance that it won’t happen either. A very, very small chance. It could have happened that all the Egyptians chose good, and then the Holy One’s prophecy in advance would have failed. Yes, that could happen.

[Speaker B] You don’t need all of them. It’s enough that there be—

[Rabbi Michael Abraham] But the chance of that is so tiny that you can safely bet on it. It’s like the chance that a soccer ball will go through a wall.

[Speaker B] You just need enough Egyptians.

[Rabbi Michael Abraham] I didn’t understand.

[Speaker B] There has to be a large enough number of Egyptians who want to enslave them. Not one percent, two, ten, twenty. It has to be a sufficiently high percentage for it to work.

[Rabbi Michael Abraham] I’m talking about that percentage. Suppose the Holy One, blessed be He, says that eighty percent—how did the Holy One, blessed be He, know that there really would be—

[Speaker B] Such a high percentage who would enslave the Jewish people?

[Rabbi Michael Abraham] It could be that only sixty percent would come out and not eighty percent, because their choices were such that they didn’t align exactly with the expectation. Fine, that can happen. It could be that all of them chose good; that too can happen, even though the chance is truly negligible. So in principle, if I set the weights so that eighty percent of the Egyptians will enslave the Jewish people, I can safely say that the Egyptians will enslave the Jewish people. Collectively, it will happen. The chance that it won’t happen is negligible. It exists, but it’s negligible. So in principle it’s true that this prophecy is not deterministic, but the law of large numbers says: it will happen. Think about this: can the Holy One, blessed be He, predict in advance—or can I predict in advance—that when I kick a ball toward a wall, the ball will not pass through the wall to the other side? Every one of you would say yes. Obviously you can predict that in advance. Even though quantum theory says there is a very, very small chance that this won’t be so. True, but it’s so small that it’s uninteresting. It won’t happen. For all practical purposes, the probability is zero. That’s exactly the meaning of collective prophecy—or not prophecy here, but planning. Here the Holy One, blessed be He, not only predicted what would happen, He also created what would happen. And still, since the creation works by statistically biasing the weights, He can predict in advance what will happen, and one can still come with claims against each Egyptian who enslaved the Jewish people. There is no contradiction. It’s a bit tricky, but I think it’s clear that it’s true. Okay, we’ll stop here.

[Speaker C] Rabbi, still, Maimonides’ formulation is very sharp. He explicitly wrote: “And there is no one who compels him, nor decrees upon him, nor draws him to either of the two sides.”

[Rabbi Michael Abraham] “Decrees,” yes—but “draws”? “Decrees upon him” means dictates to him what to do. “Draws him” means activates him in practice. There is neither this nor that—and there is still statistics.

[Speaker C] Rabbi, why can’t one also explain it by saying that obviously, if there is—say eighty percent—you have one force pulling you very strongly toward one of the sides, but in the end when you stand before the decision whether to yield to that force or not yield, in that decision you are completely free, while taking all the existing conditions into account?

[Rabbi Michael Abraham] You are free in the sense that you can decide this way or that. Of course—that’s what I’m saying. But now if you put a million people at that same crossroads, you’ll discover that eighty percent chose in the direction the statistics predicted.

[Speaker C] Yes, yes, that’s a real problem.

[Rabbi Michael Abraham] And that’s exactly my claim: every individual really is free. Even though in the large-scale statistics it comes out eighty percent, still eighty percent will do what was foretold in advance that they would do.

[Speaker D] Can one really say this about a human society, and Egyptian society in particular, in a monarchical period, where in the end the decisions here are independent—

[Rabbi Michael Abraham] I’m trying to propose a model for how it could be that the Holy One, blessed be He, can predetermine something even though every individual has free choice.

[Speaker D] In principle, yes, but with Egypt it fits less well.

[Rabbi Michael Abraham] Even under a monarchy, in principle—think about the Nazis. With the Nazis too there was basically monarchical rule in a certain sense; it was an authoritarian regime, right? The regime decided, and whoever went against it got hit. And still, there were people who nevertheless chose to resist—passively, actively, to a greater or lesser degree—because they understood that these were acts of horror. So even in such a situation the weights are very, very heavy in a certain direction, but each person still has a choice, and therefore—

[Speaker D] No, that’s fine, I agree there is choice. But you can’t build on the statistics of the distribution. What, the claim is that there will be some forty percent here who succeed and so on—but maybe not. If one person influences all the others very strongly because he happens to be the king, then maybe I can’t guarantee that forty percent will do something evil.

[Rabbi Michael Abraham] And that’s why I said—what I proposed before was some kind of model. But that model reflects a phenomenon that is true even where the model itself isn’t relevant. You’re describing a situation in which the choices are simply not independent. When choices are not independent, the law of large numbers does not exist, because not every Egyptian makes decisions independently. There’s correlation between the decisions. The king dictates everything. And that’s true. But now let’s look at the Egyptian’s decision whether to submit to the king’s dictate or not. Because in the end he can say that it violates his conscience and bear the price, and resist. Of course that is very hard to do; let’s say the chance that someone would do it is two percent. Fine. But each Egyptian still has a two percent chance of resisting.

[Speaker D] And clearly most of them won’t resist.

[Rabbi Michael Abraham] So that means it can be predicted in advance, even though regarding each individual Egyptian one can still come to him and say: why did you do that? Just like they judged the Nazis at Nuremberg.

[Speaker D] No, but even if there is choice, you can still say there is very high correlation, even if there is choice.

[Rabbi Michael Abraham] Okay, so what?

[Speaker D] It’s not deterministic, but it’s correlation. Right.

[Rabbi Michael Abraham] And still I claim that on the one hand you can predict what will happen, and on the other hand you can come with claims against each person for what he did. What you can’t do is apply my model of the law of large numbers, because here there is dependence between the trials. I used the law of large numbers to illustrate an idea that doesn’t actually require the law of large numbers; I apply it to this case too, even though here the law of large numbers doesn’t exist. That’s what I’m saying. And I can dictate it—like with the Nazis. Why were the Nazis tried at Nuremberg? What did people want from them? If someone didn’t obey an order, they’d shoot him in the head.

[Speaker D] Okay, because there is choice. But then apparently prediction is no longer possible. Why? Because I don’t have the conditions under which I can—

[Rabbi Michael Abraham] No, you can predict what will happen. If you had asked me what would happen in Nazi Germany, and you had described all the phenomena, I would have told you that acts of horror would happen there. Even though each individual German had a choice; in principle he could have resisted. It’s very hard to resist, and therefore statistically there will be—

[Speaker D] Very, very many Germans who won’t resist. No, but because there is correlation, it would be enough if Hitler had not existed but someone else had been in his place, and then the whole story might have looked different. It’s hard to predict under high correlation.

[Rabbi Michael Abraham] But Hitler did exist. The Holy One, blessed be He, sets up Hitler, and now the question is whether the Germans will enslave Israel or not. Still, regarding each individual German one can make claims. Even though I can tell you in advance that the Germans will murder millions of Jews. There—you have prediction without the law of large numbers.

[Speaker D] So what we gained is that Hitler himself had no choice, because basically—

[Rabbi Michael Abraham] God has to start with something. If you look at Hitler as a person, then fine, yes. Then He took away his choice. But now we’re not making claims against Hitler; we’re making claims against ordinary Germans. When you make claims against Hitler, then I’ll need to make the model about Hitler himself. But if you’re talking about ordinary Germans, then let’s treat Hitler as part of the circumstances. And Hitler the Holy One, blessed be He, put in place—deterministically. But the Germans still could have resisted Hitler. “We are not willing to do these atrocities,” full stop. But the chance of that is very small, and therefore I could predict in advance that millions of Jews would be murdered, and still I judge each individual German for what he did.

[Speaker C] If all the Germans had, so to speak, had the mentality of Abraham our father, then—

[Rabbi Michael Abraham] What would have happened? I said: with a very low probability.

[Speaker C] Even before they acted, that was already part of their wickedness—not only what they did, but what they were, their culture.

[Rabbi Michael Abraham] No, that’s taking me back again to determinism. No. The wickedness is in what they chose. Once they chose, they became wicked. I’m not hanging it on something prior to that. Yes, of course, in that choice itself there is a certain chance that this prophecy would not be fulfilled, because it is a statistical prophecy. A very, very small chance that all the Egyptians would choose good—like the ball passing through the wall. Fine. But you can still give this kind of deterministic prediction; it works excellently in physics, and it works the same way regarding the Egyptians, even though there is a very, very small chance that the prediction won’t be fulfilled. Okay.

[Speaker C] No, what I meant to ask was that the claim against the Egyptians and against the Germans and all such people is not necessarily about “it was imposed on us statistically.” Rather, the very fact that you are as you are—if all of you had been Abraham our father, a culture of righteousness and kindness and love—then the statistics would be like taking the die and weighting it so that it won’t be balanced, but will fall ninety percent of the time on a particular number.

[Rabbi Michael Abraham] In other words, that’s basically what I said. Given the whole Nazi structure and everything, still a person like Abraham our father would throw himself into the fiery furnace and not do it. And the fact that ninety-eight percent of you did do it—that is what I’m holding against you. Even though it really was very hard; maybe I too would not have passed such a test. Because that still counts as free choice for a human being. Okay? May I take a question?

[Speaker E] Yes. So just to summarize what happened in the lecture: you gave Maimonides’ answer to the issue, to the claim that Maimonides proposes, and then you suggested a more detailed model for what Maimonides said?

[Rabbi Michael Abraham] Yes. That’s what Maimonides means. Maimonides means that the prophecy—as he writes—the prophecy was not about a particular individual; it was a statistical prophecy. The Egyptians, in principle, would enslave the Jewish people. Therefore, says Maimonides, this does not contradict my ability to come with claims against each Egyptian who took part in it and hold him accountable for it.

[Speaker F] Yes, but everything you used was in concepts that were created after Maimonides.

[Rabbi Michael Abraham] No, that’s not the point. This understanding could have been understood even in Maimonides’ time. Today we have much better tools to analyze it and explain it. But I think people back then too could have understood it. They didn’t know the law of large numbers, they didn’t know all that, but intuitively you understand that this is how it works.

[Speaker E] I understand.

[Speaker G] Sorry, unlike, for example, rolling a die, where according to the law of large numbers you can predict the outcomes, here the very fact that the Holy One, blessed be He, affected the weights for the Egyptians to enslave the Jewish people means that He set them up facing the option of enslaving the nation—when there was no reason that option had to exist in the first place. Because the Egyptians in relation to the Israelites had a million options. That’s exactly the meaning of playing with the weights, right?

[Rabbi Michael Abraham] But they still had the choice not to do it.

[Speaker G] Right, but He set them up with that option, which maybe otherwise would hardly even have existed. Right.

[Rabbi Michael Abraham] And that’s the meaning of what He said: “Your offspring shall be strangers in a land not theirs, and they shall enslave them and oppress them for four hundred years”—that the Holy One, blessed be He, created the circumstances that caused the Egyptians to do that. But that does not contradict the continuation: “and also the nation that they shall serve I will judge.” It is still possible to judge the Egyptians for what they did. That is exactly the point. That is exactly what I came to explain here: that on the one hand the Holy One, blessed be He, basically created this outcome, and on the other hand one can still come with claims against each person who took part in it. It’s a little tricky, but it’s clearly true. Next time we’ll see the implications of this idea; it has very broad and interesting implications in different areas. And it sounds simple when I say it, but the fact is that people miss it in many contexts—this possibility, this analysis. Okay. Have a peaceful Sabbath. Goodbye.