Artificial Intelligence – Lesson 10 – Rabbi Michael Abraham

[Rabbi Michael Abraham] Maybe we should summarize where we’re up to, since we had a break. So basically I began by trying to define what a human being is. I talked about dualism, I talked about the physical and the mental. After that I tried to neutralize the question of dualism, because I said it could be that the mental really emerges from the physical. I don’t think that’s true, but for the purposes of our discussions it doesn’t matter. So I’m not getting into the details now, this is just a general summary. Now the question is how all this relates to a computer. A computer obviously has the computational dimension, but it doesn’t have the semantics of the matter, the dimension of—how should I put it—the understanding of why exactly we’re doing this process, or how exactly we’re doing the calculation, say, or the thinking. Rather, it performs a mechanical action and produces a result, but to give that action meaning or significance—for that you need some kind of, let’s call it, human mental dimension. I’m careful not to say soul or anything like that, because I don’t want to drag us back into dualism. So after that I moved into the question of what thought is, and I talked about semantics versus syntax. I brought various examples of this in order to show that it’s possible to perform actions that imitate thinking, but they don’t really deserve to be called thinking. I talked about whether water has intelligence. If you remember, we had all sorts of arguments about that. And I argued that water supposedly solves a very complicated equation, the Navier-Stokes equation. So on the face of it, it’s really brilliant, because no mathematician or physicist knows how to solve those equations, at least beyond the trivial cases. But it’s clear to all of us that this isn’t right—you can’t talk about the intelligence of water. The question is why not, if it’s supposedly solving the equations. Look, see how it flows; its flow is actually described by the formula of the solution. So the claim is that it simply behaves that way, but it doesn’t have the dimension of understanding, the mental dimension that is actually responsible for the form of the calculation; it’s not performing a calculation. It simply behaves as its nature dictates. And of course that brings us back to the question of what the difference is between that and a computer. Because with a computer, that’s what it does. It runs electrons, does all sorts of things, and something comes out, some process. The meaning of that process—saying that what happened here is actually the exercise two plus five equals seven—that meaning is supplied only by the human being who uses the computer. The computer in itself is just running electrons. Therefore I argued that one cannot talk about the intelligence of a computer. That is, a computer is not really measured, and cannot be measured, in terms of intelligence. That’s basically my claim—it’s like water. After that I talked about the Chinese room and the Turing test, where the person sitting in the Chinese room gets questions in Chinese, gives answers in Chinese without knowing Chinese, but gets zapped for every wrong answer, and if he has infinite time then in the end he’ll somehow learn, in a technical way, to match a relevant answer to every question, while still not understanding either what the question says or what the answer says. He only learned to match them—a kind of input-output function. About such a person too, what I argued—that’s John Searle’s example—about such a person too one cannot say that he knows Chinese, even though he performs the computational acts that a Chinese speaker performs. That is, he too matches a relevant answer to a question. In that sense he behaves like a Chinese speaker. But since he lacks understanding, the mental dimension that actually—meaning, he is a person, he has a mental dimension, but his mental dimension is not involved in the process, the process is just a technical one—therefore one also cannot say that he understands Chinese. That was basically the claim, and what I sharpened here is that when we talk about acts of thinking it’s very important to distinguish between their technical description—what I do—and the thinking that carries out that technical process, which is not the same thing even though from the outside it looks identical. Examples of semantics versus syntax—if you remember the MIU puzzle and things of that kind—and then I moved on to talk about creativity and said that creativity is basically a kind of thought that is non-algorithmic, meaning something involving some kind of leap that you cannot derive logically, the conclusion from the premises, but somehow you guess the conclusion or arrive at the conclusion in some way that I have no ability to mechanize, and therefore there is here, basically, what I would call a creative act. I gave examples of this through the concept of abduction—how we get from scientific observations to a theory that explains them. So I said there is both a process of induction there, to reach the general law of which these are particular cases, and also a process of abduction, to arrive at a theory that explains these cases. And abduction and induction are not the same thing. Both, however, contain a dimension of creativity, and therefore supposedly a computer won’t be able to do such things, and maybe that gives us some clue to the concept of intelligence. Something that characterizes human beings and does not characterize devices—rocks won’t perform a creative act. The computer solves an equation. That is, a creative act is something we would usually attribute only to thinking creatures. Okay? That was basically the claim. I brought examples of creative thinking through the solution to Hofstadter’s MIU puzzle. We talked about the domino and chessboard puzzle, if you remember—how you take an eight-by-eight chessboard, remove the square on both ends of the diagonal, one square here and one square here, so now 62 squares remain. Then I take 31 dominoes and try to cover the 62 squares. In terms of area that’s fine—31 dominoes can cover 62 squares. The question is whether there is actually a way in practice to do it. And the solution to that puzzle is a creative solution. What does that mean? The solution I presented was—I tried it a little, made various attempts and so on, didn’t manage, but I didn’t know how to prove that it was impossible or make sure that it really couldn’t be done. But if you think about it creatively for a moment, you say: let’s color the chessboard squares black and white. Okay? And now when we removed the two squares on both sides of the diagonal, those are two squares of the same color, right? Because it’s the same diagonal. Two squares of the same color—say they’re both black. So now on the board I have 32 white squares and 30 black squares. But every domino you place always covers one white square and one black square—there’s no way it can cover two squares of the same color, right? That means that with 31 dominoes it’s impossible to cover this board, which is what had to be proved. Now the creative step that was made here, which turned the problem into something trivial once you made that step—that step is to color the board black and white. If we weren’t familiar with the game of chess, no one would ever think to do such a thing. Why color the squares? Why is that even relevant? I think no one would think of such a thing if we weren’t familiar with boards of that kind that are colored black and white. And that’s a step that requires a measure of creativity; that is, there’s no systematic route from the problem to that step and through it to the solution. Therefore it’s a solution I would call creative. I brought some other examples of things like this too—the cutting of two convex shapes, if you remember, all sorts of things of that kind. Now we talked about the concept of judgment, and I compared judgment to free choice. What does that mean? Judgment reflects exactly the creative dimension I described earlier, because a mechanical action is an action with a deterministic result; there is a deterministic route from the problem to the solution. In a situation where some creative step is required, that means there is some kind of judgment here that is not calculation; rather, you have to decide that something is relevant even though you have no systematic way to show it, meaning no systematic way. Meaning, you also have no systematic way to arrive at it. Therefore judgment is actually tied at the navel to what I earlier called creativity. And the ability to exercise judgment basically comes to expression wherever the thinking being done is not mechanistic, not deterministic, but rather requires some leap that demands creativity, and that basically parallels the concept of judgment. In that sense it resembles free choice a bit. Judgment is in thought, and free choice is in will, but both are similar in the sense that they depart from mechanistic deterministic functioning. Okay, now of course one can discuss whether behind creative thought there is some mechanism, we just haven’t managed to formulate it or conceptualize it, but behind it there really is some mechanism. So that connects to Kahneman’s System 1 and System 2, but we’ll come back to that later, so for now I’m setting that aside. I talked—just to finish the summary—I talked about three modes of thought: deduction, induction, and analogy. Deduction is from the general to the particular, induction is from the particular to the general, and analogy is from one particular to another. We also talked about abduction, but that’s a separate story. In deduction the conclusion follows necessarily from the premises; that reflects deterministic thinking. Induction and analogy reflect creative thinking. How do you make an analogy between cases or between objects—maybe it’s similar, maybe it isn’t. There’s no systematic mechanical way to arrive at the conclusion that this analogy is really relevant. There is a creative dimension here. Same with induction. All scientific processes like scientific induction are basically creative processes, unlike mathematical proof, which is supposedly a mechanical process. That’s not precise, because even in mathematical proof you have to think of which mechanical process to carry out. The fact that the process is mechanical still doesn’t mean you have a systematic way to arrive at it, but we’ll talk about that later. In any case, after that I described deduction, or analytic thinking, and I said that the certainty accompanying deduction, or logic, or mathematics, stems from the fact that the conclusion can be derived mechanically from the premises. There is nothing in the conclusion beyond what was already latent in the premises, and therefore the conclusion follows necessarily from the premises because it is simply contained in them. If you accept the premises then in particular it is contained there—not always obviously, but after the proof it becomes clear—you have in effect also accepted the conclusion. Therefore deduction is a necessary process because it doesn’t add information for me. This is the uncertainty principle: the degree of certainty times the amount of information added to us in the process is constant. Therefore if the degree of certainty is one, the amount of information added will be zero. If the information is infinite, then the certainty will be zero. And in between there is some interplay where we can decide: if we want high certainty, we’ll have to make do with little information. If we’re willing to give up a degree of certainty, we can arrive at more information. That is, the degree of speculation basically determines how much information I will allow myself to extract from the process. And again, these are all different ways of looking at the creative dimension as opposed to the mechanical dimension of thought. In the end—and with this I’ll finish the summary—I described the process of a person’s maturation, and also the history of the West. I said that basically the child is dogmatic; he accepts what he is told because he does not use critical thinking. What his parents or teachers tell him is probably correct because they know. Then comes the adolescent and says, “Who told you that? Prove it.” Then he matures and reaches the conclusion that nothing can be proved. Why not? Because every proof is based on first assumptions. Now if you are unwilling to accept things without proof, then you won’t be able to accept the first assumptions. But without accepting first assumptions, what will you be able to prove? You can’t prove anything if you’re unwilling to accept any first assumption, because every proof begins from first assumptions that you accept. Therefore, someone who sticks only to things that are certain, things that can be proved, will remain without information. Again, the uncertainty principle. If you want full certainty, there is no information. You have to give up a level of certainty in order to be able to receive, adopt, or arrive at information. That’s the cruel game forced upon us. And I said there are three ways to mature from this adolescent point. One way is to say: okay, only a certain thing is acceptable, but nothing is certain, therefore nothing is acceptable. Be a skeptic, a postmodernist, call it what you like. The second way is fundamentalism, which says: it’s not true that there’s nothing we can be certain about. There is what Allah said, what the rebbe said, what the qadi said, it doesn’t matter, the sheikh, whoever—it’s above all critical thinking, it’s certainly true, and therefore I can relax. I have certainty—yes, “he who believes is not afraid.” So this approach basically says that indeed only something certain is acceptable, but it does not accept the second assumption that nothing is certain. Not true, because we have ways beyond logic to arrive at truths. Some kind of spiritual charisma, revelation of Elijah, revelation of the Holy One, blessed be He, however you want to call it. And the third form of maturity says that I’m not willing to accept things that are beyond reason, let’s call it that, but I am willing to accept things I don’t have certainty about. This I called synthetic maturity, which basically means I’m willing to accept things even if the step toward them was a creative step, and not only when I have a rigorous logical proof for the matter. Even in a place where some creative thought is required, where my common sense tells me that this thing is right, that too is fine for me, acceptable. It’s not certain that it’s true, but I accept it and act accordingly, and so on. That is synthetic maturity. In the end—now I’m moving on, up to here was the summary—now I want to explain what all this actually means. What this basically means is that when we look at rational thinking, rational thinking is always built on arguments. Arguments basically start from first assumptions, from axioms, and by means of logical rules derive conclusions from them, right? That’s rational thinking. Therefore many times, when you try to define who is a rational person or what rational thinking is, it will be very hard for you to do so. Because basically the only thing you can really dismiss out of hand is if someone makes a logical mistake. So logical thinking, or let’s call it validity of an argument, deriving a conclusion from premises—that is rational thinking, that’s clear. But that’s too thin a definition of rational thinking, because it basically means that anyone, no matter what his first assumptions are, so long as he derives from them consistently the relevant conclusion, then he is a rational person. Meaning, a person can assume there are fourteen demons on the right, thirteen angels on the left, each angel equals two demons, therefore the angels will defeat the demons. That is a valid logical argument—the conclusion follows from the premises. Very often, when we relate to statements like that, we’ll treat them as irrational statements. Why are they irrational? Because of their premises. But once you’ve accepted the premises, the conclusion follows from the premises. Now, how do you measure the rationality of premises? Whatever seems rational to me is rational, and whatever doesn’t seem rational to me is not rational? That’s a bit tautological. So then what—how do I measure, how can I set standards for rational thinking beyond the logical derivation of the conclusion from the premises? How can I judge the adoption of the premises themselves? And that once again brings us back to the fact that indeed the skeptic will say no, I can’t, and therefore premises are not something one can really stand behind, and consequently the conclusion that follows from them doesn’t interest me either, because if I have no trust in the premises then why should I care about the conclusion? And that is the skeptical outlook. But if we are not skeptics, and if we do accept things, and are nevertheless willing to regard some claims as truer than others, then we have to assume here—we are implicitly assuming—that some premises are preferable to others. Because anyone can present his position as a position based on certain premises from which he derives a conclusion. In that sense we will never succeed in deciding who is right and who is wrong. We have to judge the premises. Now the question is: how does one judge premises? After all there is no logical argument that proves them, and therefore I have no way to judge—apparently no way to judge—whether those premises are true or false. And this is where intuition or common sense comes in. Intuition or common sense are basically the tools by which we judge premises or adopt premises. This premise—I had a good reason for it. And that’s all, therefore it is a correct premise. Meaning, not because there is a logical argument leading to it. There isn’t one. It is a premise; the logical arguments will begin from it. But the premise itself I adopt because my reasoning tells me so, because my common sense tells me so, and therefore I adopt that premise. What this really means is that when we judge a certain thesis or a certain position, it is not enough to judge the consistency—whether the conclusion follows from the premises, or whether there is no contradiction among the various premises—we also have to judge the premises themselves. Now, how do we do that? We have an intuition that says this is right and that is not right; someone else has a different intuition. What do you say to that? All you can say is that it doesn’t fit my intuition. So what? Who said my intuition is preferable to his intuition? Those are always the kinds of arguments that in the end lead people to skepticism. Yes.

[Speaker B] I don’t quite understand. I mean, if my intuition tells me that I’m right, then why should I suddenly give any respect to the other person’s intuition? The Rabbi is saying as though I’m saying “my intuition.”

[Rabbi Michael Abraham] You won’t give it respect, but the question is whether you can determine in some objective sense that you are more rational than he is.

[Speaker B] I’m not in court. I have to answer to myself. I’m one hundred percent convinced that my intuition is right. Why should I care that maybe the other one is right? In my eyes he isn’t right.

[Rabbi Michael Abraham] One hundred percent sounds exaggerated to me, but yes, I too go with my intuitions. But I’m saying again: no problem, go with your intuition. But regarding the question of who is rational—that’s not a question asked from my perspective on myself, but rather a question asked from some objective point of view. I look at different outlooks and ask whether I can say something about some outlooks, that they are rational and others are less rational. Here it’s difficult, difficult to determine such a thing. I can determine what my own position is and accept it, no problem.

[Speaker B] So that really proves that we aren’t truly rational creatures—it’s not Elijah. Okay.

[Rabbi Michael Abraham] I don’t think it proves that we are not rational creatures, and I claim there is a more abstract or softer definition of rationality. Common sense. When I see something and someone else doesn’t see it, then he is mistaken.

[Speaker B] But the Rabbi needs to point out to us what common sense is. It’s a semantic expression. But we have either facts of reality, or a priori logic, or emotion—intuition and emotion are the same thing—that’s what we have, there aren’t others.

[Rabbi Michael Abraham] Allow me not to go over that argument again. What you call emotion, I divide into two: emotion and intuition.

[Speaker B] Fine, so why shouldn’t I just go along with dividing emotion into seven hundred emotions? It’s still emotion.

[Rabbi Michael Abraham] Those are not two kinds of emotions. Don’t put words in my mouth. I did not divide it into two kinds of emotions.

[Speaker B] Is it facts of reality? No. Is it a priori?

[Rabbi Michael Abraham] Certainly—it is facts of reality, yes, facts of reality.

[Speaker B] But the facts will be facts for both of us. There’s no argument that we all know the facts. We’re talking about—

[Rabbi Michael Abraham] Why no argument? You don’t know the facts and I do.

[Speaker B] No, but what facts can one know? Where every electron is and what moves it—we don’t know.

[Rabbi Michael Abraham] The fact that I know is that it is forbidden to murder Jews. The Nazi does not know that fact, and I claim that I am right and he is wrong. Not that I have one emotion and he has another.

[Speaker B] Of course that’s—so that’s unrelated. Why? Exactly—of course values are emotions, of course values are emotions.

[Rabbi Michael Abraham] Fine, so let’s stop here, because we’ve ground through this argument dozens of times, so we won’t go back to it again. Okay, so in the end the claim is that rational thinking is always built from premises from which I derive conclusions. And the judgment of the derivation is by means of logical tools. The judgment of the premises—assuming they can be judged, and I claim they can, and that this is not emotion—then it is basically something else. Common sense, intuition, I don’t know what you want to call it. Whatever you call it. Now I will come back to this issue again, but I want to ask a question that will hint to us why all these discussions are connected to the topic of the series. Because now I’m going to ask myself what, out of this whole process, a computer can do. So a computer usually—I’m talking about a classical computer, leave artificial intelligence and things like that aside for the moment—an ordinary computer with software, what we knew until not many years ago—a computer or a computer program basically performs deterministic calculation. That is basically a logical process, right? A computational process. Okay? Which basically says: you start from some set of input, you have tools—call them inference tools—and from that input you derive an answer, derive output, the result of the calculation. Okay? So basically the computer performs the action of moving from premises to conclusions, the mechanical part of thought. Can a computer, or a non-human creature, also do the intuitive part, the creative part, or everything we’ve been talking about until now? That’s a big question. An ordinary computer certainly cannot. Artificial intelligence—that is exactly the difference between it and an ordinary computer. But for that we’ll have to proceed in an orderly way and explain what artificial intelligence is, so I’m stopping here for now; we’re still in the introduction. Now since we are in the month of Elul, I thought we should still take some kind of break connected to the season, but I’ll present it from an angle connected a bit to Yom Kippur. This is some line of thought I already spoke about many years ago in Yeruham; I also wrote about it. Some of you may already have seen or heard it, I don’t know—about the two goats on Yom Kippur, and I connect it to the things we’ve spoken about until now. I’m not staking my life on how much this is a homiletic reading or whether it’s really a true interpretation—I’m not entirely sure. There’s a bit of a homiletic flavor here. You judge; I don’t know. Because for me, a homily is a dirty word. A homily is a curse. Okay, so maybe I’ll start—I’ll share the screen—I want to start with the portion of Acharei Mot. וידבר ה’ אל משה אחרי מות שני בני אהרון בקרבתם לפני ה’ וימותו. ויאמר ה’ אל משה דבר אל אהרון אחיך ואל יבוא בכל עת אל הקודש מבית לפרוכת אל פני הכפורת אשר על הארון ולא ימות, כי בענן אראה על הכפורת. בזאת יבוא אהרון אל הקודש בפר בן בקר לחטאת ואיל לעולה. כתונת בד קודש ילבש ומכנסי בד יהיו על בשרו ואבנט בד יחגור ובמצנפת בד יצנוף בגדי קודש הם, ורחץ במים את בשרו ולבשם. ומאת עדת בני ישראל יקח שני שעירים (And the Lord spoke to Moses after the death of the two sons of Aaron, when they came near before the Lord and died… And the Lord said to Moses: Speak to Aaron your brother, that he not come at all times into the sanctuary… Thus shall Aaron come into the sanctuary… and from the congregation of the children of Israel he shall take two goats), and then the section of the two goats begins, and all the sacrifices of Yom Kippur, the whole Yom Kippur service. Then the whole description of the Yom Kippur service, and here it says: והייתה לכם לחוקת עולם בחודש השביעי בעשור לחודש תענו את נפשותיכם וכל מלאכה לא תעשו האזרח והגר הגר בתוככם. כי ביום הזה יכפר עליכם לטהר אתכם מכל חטאותיכם לפני ה’ תטהרו. שבת שבתון היא לכם ועיניתם את נפשותיכם חוקת עולם. וכיפר הכהן אשר ימשח אותו ואשר ימלא את ידו לכהן תחת אביו ולבש את בגדי הבד בגדי הקודש. וכיפר את מקדש הקודש ואת אוהל מועד ואת המזבח יכפר ועל הכהנים ועל כל עם הקהל יכפר (And this shall be for you an eternal statute: in the seventh month, on the tenth day of the month, you shall afflict yourselves… For on this day he shall atone for you, to purify you… And the priest who is anointed… shall make atonement for the holy sanctuary, and for the Tent of Meeting, and for the altar he shall make atonement, and for the priests and for all the people of the assembly he shall make atonement). Those are three stages: to atone for the sanctuary, to atone for the priests, and to atone for all the people. והייתה זאת לכם לחוקת עולם לכפר על בני ישראל מכל חטאותם אחת בשנה, ויעש כאשר ציווה ה’ את משה (And this shall be for you an eternal statute, to atone for the children of Israel from all their sins once a year; and he did as the Lord commanded Moses). That is basically the section in broad outline. Now, on the face of it, one has to notice several interesting points. First of all, Yom Kippur is not mentioned here at all, nor even a date. It appears only at the end. At the end: once a year, in the seventh month, on the tenth day of the month, an eternal statute, you shall afflict yourselves, and so on—and then also do the Yom Kippur service. Only at the end does it say to do this on Yom Kippur. How is it presented at the beginning? אחרי מות שני בני אהרון בקרבתם לפני ה’ וימותו—after the death of Aaron’s two sons when they drew near before the Lord and died. Why did they die? Because they entered the holy in an improper way. Then the Holy One, blessed be He, says to Moses: ויאמר ה’ אל משה דבר אל אהרון אחיך ואל יבוא בכל עת אל הקודש מבית לפרוכת and so on, ולא ימות כי בענן אראה על הכפורת—don’t make the mistake your sons made, entering the holy rashly. So how should he enter? Because otherwise he’ll die like them. So how should he? בזאת יבוא אהרון אל הקודש—thus shall Aaron come into the holy—and then all the details there of the Yom Kippur service. Meaning, the Yom Kippur service is not really the Yom Kippur service. The Yom Kippur service is the way one enters the holy properly. Aaron’s sons died because they entered the holy without this—not in the right way, but in some other way—and therefore they died. And whoever wants to enter the holy and not die, this is the procedure he must follow. The two goats and the additional offerings and all the sprinklings and immersions and garments, white garments and golden garments and all the details of the Yom Kippur service. Only at the end does the Torah say: once a year, on Yom Kippur, on the tenth of the seventh month, do this. So in principle, any time Aaron wants to enter the holy, no problem—you can enter if you first perform this procedure. On Yom Kippur you must do this—not if you want to enter the holy. On Yom Kippur one enters the holy. Of course, if one wants to enter the holy, one does it this way. But notice: this service is not really the Yom Kippur service at all. What has to be done on Yom Kippur is to enter the holy. That is the Yom Kippur service. The sacrificial service that accompanies entry into the holy is simply the way one enters in order not to die. So this is a somewhat different perspective on the whole service of Yom Kippur. Now, the essence of the sacrificial service on Yom Kippur is the two goats. Yes—one goat goes into the innermost place, and the other goes to Azazel, outside. So simply speaking, it seems that the essence of the Yom Kippur service is the inner goat, which accompanies the priest’s entry into the holy place. But it turns out—and this is what the Talmud says—that our sins, almost all of them—perhaps not the impurity of the sanctuary and its holy things—but our sins, all our sins, Tractate Shevuot deals with this in the first chapter, are atoned for by the scapegoat. The scapegoat—yes—it carries all our sins into the wilderness. Okay? It is specifically that one that atones for all our sins. How does this strange thing happen with the scapegoat? What is the meaning of the atonement? Why isn’t it the inner goat? And what is the meaning of the goats altogether? So I want to address the matter of the goats a little. So let’s perhaps start with Ibn Ezra there on these verses in Acharei Mot. He writes as follows: ואמר רב שמואל, אף על פי שכתוב בשעיר החטאת שהוא לה’ וגם השעיר המשתלח הוא לה’ ואין צריך. I don’t know whether “Rabbi Shmuel” here is Rashbam, I don’t know. In any case, Rabbi Shmuel basically says: don’t be mistaken—the sin-offering goat, the one that goes into the innermost sanctuary, is for the Lord. But the sent-away goat—you think it isn’t for the Lord because it goes somewhere else? No, no, that too is for the Lord. There are no sacrifices we offer to someone other than the Holy One, blessed be He. So Ibn Ezra says: ואין צריך—“and there is no need”; that is Rabbi Shmuel’s interpretation. Ibn Ezra says: ואין צריך. למה? כי המשתלח איננו קורבן, כי לא ישחט—there is no need, because the sent-away goat is not a sacrifice, since it is not slaughtered. Yes, we do not slaughter it. So if it’s not a sacrifice, then you don’t need to be troubled by the idea that there is a sacrifice here to some being other than the Holy One, blessed be He, because it is not a sacrifice. So there is no obligation, no necessity, to say that the sent-away goat is also for the Lord, because it isn’t a sacrifice, so there’s no reason to be concerned about that at all. And then: ואם יכולת להבין הסוד שהוא אחר מילת עזאזל תדע סודו וסוד שמו כי יש לו חברים במקרא. ואני אגלה לך קצת הסוד ברמז, בהיותך בן שלושים ושלוש תדענו—if you can understand the secret behind the word Azazel, then you will know its secret and the secret of its name, for it has companions in Scripture. And I will reveal a bit of the secret to you by hint: when you are thirty-three, you will know it. Yes, these are Ibn Ezra’s riddles. So he says: if you can understand the secret of the word Azazel, then you’ll understand the secret of the sent-away goat, what the idea behind it is. And he gives a hint: when you are thirty-three, you will know it. What does he mean? So Nachmanides there writes as follows: והנה רבי אברהם נאמן רוח מכסה דבר אבל אני הרכיל מגלה סודו, שכבר גילו אותו רבותינו במקומות רבים—Rabbi Abraham is of a faithful spirit and conceals a matter, but I, the talebearer, reveal his secret, for our Sages already revealed it in many places. ומפורש מזה בפרקי רבי אליעזר הגדול, לפיכך היו נותנים לו לסמאל שוחד ביום הכיפורים שלא לבטל את קורבנה. שנאמר גורל אחד לה’ וגורל אחד לעזאזל. גורלו של הקדוש ברוך הוא לקורבן עולה וגורלו של עזאזל שעיר חטאת, וכל עוונותיהם של ישראל עליו—therefore they would give Samael a bribe on Yom Kippur so that he would not prevent the offering, as it says: one lot for the Lord and one lot for Azazel. The lot of the Holy One, blessed be He, is for an offering, and the lot of Azazel is the sin-goat, and all the sins of Israel are upon it. What is he saying? As Ibn Ezra says, the scapegoat is not for the Holy One, blessed be He. Rabbi Shmuel is wrong. So for whom is it? For Samael, for Satan. They give him a bribe on Yom Kippur so he won’t interfere with our atonement. But in an extremely strange way, the scapegoat is the one upon which all the sins of Israel are placed—not the inner goat. I would have thought that the inner goat is the one that atones. The scapegoat gives some kind of bribe to Satan so he won’t interfere with our obtaining atonement through the inner goat. No, no. The scapegoat is the one that atones for us. והנה הודיענו שמו ומעשהו, וזה סוד העניין, כי היו עובדי אלוהים אחרים הם המלאכים, עושים להם קורבנות והם להם לריח ניחוח. והנה התורה אסרה לגמרי קבלת אלוהותם וכל עבודה להם. אבל ציווה הקדוש ברוך הוא ביום הכיפורים שנשלח שעיר במדבר לשר המושל במקומות החורבן, והוא הראוי לו מפני שהוא בעליו—he belongs to ruined places, he is the master there, he rules that place, ומאצילות כוחו יבוא חורב ושממון—it is from the emanation of his power that desolation and ruin come. Not that that prince dwells in the desert and therefore it is a desert, but rather because his power is there, that is what creates desolation and ruin. כי הוא העולה לכוכבי חרב והדמים והמלחמות והמריבות והפצעים והמכות והפירוד והחורבן—he is connected with the stars of sword, bloodshed, wars, quarrels, wounds, blows, division, and destruction. ואין הכוונה בשעיר המשתלח שיהיה הקורבן מאיתנו אליו חלילה—the sent-away goat is not a sacrifice from us to him, Heaven forbid. Not a sacrifice to Satan. But rather, שתהיה כוונתנו לעשות רצון בוראנו שציוונו בכך—our intention is to do the will of our Creator who commanded us thus. And that is the meaning of the lots, says Nachmanides. Because if the priest had consecrated them verbally “for the Lord” and “for Azazel,” he would have looked as if he were serving him and making a vow in his name. But no—he would set them before the Lord at the entrance to the Tent of Meeting, because both are a gift to the Lord. Both the scapegoat and the goat for the Lord are basically a gift to the Lord, not both a sacrifice to the Lord; both are a gift to the Lord. והנה רמז לך רבי אברהם שתדע סודו כשתגיע לפסוק ולא יזבחו עוד את זבחיהם לשעירים—Rabbi Abraham hinted to you that you will know its secret when you reach the verse, “They shall no more offer their sacrifices to the goat-demons.” How did he get that? It’s a verse found thirty-three verses after the verse Ibn Ezra is discussing. “When you are thirty-three, you will know it.” Just go thirty-three verses forward and you get: ולא יזבחו עוד את זבחיהם לשעירים—they shall no more sacrifice to the goat-demons. Yes, so you are basically sending the goat to Azazel, to the goat-demons—the demons, yes, that rule the wilderness—and that will prevent us from continuing to worship idols or sin by offering our sacrifices to the goat-demons, and therefore we are atoned for by the scapegoat. That is the claim. ולא אוכל לפרש, says Nachmanides, because we would have to shut the mouths of the sophisticates in nature who follow the Greek—that is Aristotle—who denied everything except what was perceptible to him and arrogantly thought, he and his wicked students, that anything his reasoning did not grasp was not true. And here there is a very interesting hint at the end of Nachmanides’ words. Let’s think for a moment about Aristotle. How does he describe him? The Greek philosopher. He denied everything except what was perceptible to him. Right? An empiricist—he clings to observational facts, only things I perceive. And he arrogantly thought, he and his wicked students, that anything his reasoning did not grasp was not true. In short, this is someone who accepts only things we have proof for, or things we have direct observation of. Sound familiar? We talked about that in the previous lecture, though it was a month ago. This is what’s called logical positivism. Logical positivism basically says that we cannot assert any claim unless we have direct observation of it or a logical argument proving it. That is exactly the view of this Greek thinker Nachmanides describes here. And I said in that lecture that I think the Greek thinker, or Greek philosophy, is the beginning of the Enlightenment period of Western civilization, and the end of the Enlightenment period is logical positivism, which basically brought that philosophy described here by Nachmanides to its full expression. But up to this point—I want, up to this point this is just Nachmanides’ words—I want to explain a bit more. Up to here I’ve only described in other words what he himself says. So let’s take a moment and look at what happens to the scapegoat. Halakhically—legally. This is what I talked about in the yeshiva in… Yeruham. I once gave a lecture about this before Yom Kippur in the yeshiva in Yeruham. I told the guys there that usually we’re familiar with Bible hikes, you know those people who hike with the Hebrew Bible. They take the Bible and go to all sorts of places described in the Bible, and plants that appear in the Bible, and so on, and somehow use the Bible as a kind of tour guide, giving meaning to the trip. I’d rather take a hike with Rabbi Chaim—not with the Bible, with Rabbi Chaim of Brisk. We’ll go on a trip following the laws of the scapegoat. And the trip into the wilderness with the scapegoat won’t be accompanied by the Bible but by a book of Jewish law. So let’s try taking the trip from that perspective. Let’s begin by following the process the scapegoat goes through. First stage: the two goats are chosen and consecrated—they consecrate them both, as they do for every sacrifice. The Talmud in Yoma 62 says that someone who slaughtered either of these two goats outside—that is, not in the Temple courtyard—has violated the prohibition of slaughtering outside. What does that mean? That at this stage both these goats have the sanctity of a sacrifice. Therefore it is forbidden to offer them outside, forbidden to use them, benefit from them, like any sacrifice. Next stage: they take these two goats before the Lord, as we saw in Nachmanides, and cast lots. How do they do the lot? So Rashi wrote that there are two lots in the scapegoat ritual. Or let’s begin differently: the Gevurat Ari there in Yoma 39 says that over the goat that goes to the Lord they say the words “for the Lord, a sin offering,” and over the one that goes to Azazel they say nothing. That means there is one ticket that says “for the Lord, a sin offering” and one blank ticket. They draw one of the tickets and that determines which goat goes to the Lord and which to Azazel. Why? That fits what we saw in Nachmanides and Ibn Ezra—to show that we are not offering a sacrifice to Azazel. There is a sacrifice to the Lord, and the other is not for Azazel; it too is to fulfill the command of the Holy One, blessed be He, and therefore nothing is written on that ticket. But Rashi writes that no, there are two tickets, one of which says “for Azazel” and one says “for the Lord.” The lottery is done the way any other lottery is done. Why is that needed? The Gevurat Ari’s method is enough. So the later authorities explain that according to Rashi the lottery does not come only to clarify which one goes to the Lord and which to Azazel; the lottery is part of the sacrificial service of these goats. It’s not merely a matter of clarification, to determine which sacrifice is for the Lord and which for Azazel. For that, it’s enough to write on only one of the tickets. Why write on both? Because there is a procedure that must be undergone. That is, the sacrificial procedure of the two goats also includes an act of drawing lots. And that act of drawing lots must be performed even though it’s not necessary. After that, after the lot, they take the goat on which the lot for Azazel fell and tie a crimson thread to its horns. There were two crimson threads, by the way, as the medieval and later authorities note there. There was the crimson thread that was tied to the rock, by which they could see whether atonement had been achieved or not, right? Whether that thread turned white or not. But there was also a crimson thread tied to its horns. One was in the Temple, one on the horns.

[Speaker C] What? One was in the Temple, one on the horns. Not on the rock—in the Temple. It says there that the priest would hang it.

[Rabbi Michael Abraham] In the Temple, yes, the one by which we could see whether we had been atoned for or not. Now the later authorities ask: how can you tie a crimson thread on it? That’s doing work with a sacrifice. The scapegoat is also a sacrifice, it has the sanctity of a sacrifice, you may not offer it outside, you may not use a sacrifice, you may not put a burden on it, you may not do anything with it. To me that’s not such a hard question, because what do you mean? That is its service; the Torah says to do it. What’s the problem? But the very fact that they ask the question sharpens the point that they regard the scapegoat as a sacrifice. I remind you that Ibn Ezra and Nachmanides said that the scapegoat is not a sacrifice, and there is also Tosafot HaRosh in Yoma and other later authorities, and medieval authorities too, who say that it is not a sacrifice. But here the assumption is that it is a sacrifice. After the lot they do laying on of hands; the priest must lay his hand on the head of the goat. Now the Mikdash David, in the laws of the Yom Kippur service, discusses the question: what is this laying on of hands? Is this laying on of hands part of the process of repentance, or is it laying on of hands like the law in sacrifices, that every sacrifice requires the one receiving atonement to lay his hands on the sacrifice? It is part of the service of the sacrifice. Okay? So the Mikdash David says that here too it is part of the sacrificial service, the laying on of hands on the goat’s head. Again we see that even at the stage of the laying on of hands, the scapegoat is still a sacrifice. After that they confess over the goat that goes to Azazel. The priest confesses over it. “And thus he would say”—this is the third “and thus he would say.” There is confession over himself, confession over the priests, and confession over Israel. So Rabbi Chaim of Brisk says in the stencil notes—he explains that from this point on the goat no longer has the sanctity of a sacrifice. A practical implication is where they take the money from to buy the crimson thread hung on it—whether it has to come from the Temple treasury or not. Not important now; he has proofs for it, that at this point it is no longer a sacrifice.

[Speaker C] He’s probably going in the direction of Maimonides.

[Rabbi Michael Abraham] What? What does Maimonides say?

[Speaker C] In the Guide for the Perplexed, Maimonides emphasizes that the scapegoat is a ritual act and not a sacrifice.

[Rabbi Michael Abraham] It’s part of the Yom Kippur service. One moment—I’ve already brought several medieval authorities who say that. We’ll see in a moment, we’ll see. He says that now the goat no longer has the sanctity of a sacrifice. The Mikdash David claims this is a dispute among medieval authorities, because the question is whether this confession—after the laying on of hands comes confession—is that confession part of the laws of repentance that the priest performs, or part of the laws of confession over sacrifices. And again, the question is whether it is a sacrifice or not a sacrifice. The next stage, after the priest has confessed, laid on hands, and confessed, is sending the goat to the cliff. The sending is done by an איש עתי—an appointed man. What is an appointed man? It means just a regular person, not necessarily a priest. It doesn’t have to be done by a priest. What does that mean? Maybe an ordinary person. I can’t hear. An ordinary person. I didn’t understand?

[Speaker C] An ordinary layman, according to the language of the Talmud.

[Rabbi Michael Abraham] Meaning a person—

[Speaker C] It has to be someone who is not a priest.

[Rabbi Michael Abraham] Okay. Why not a priest? So I’ll continue the line of thought—apparently because the goat is no longer part of his sacrificial service; it’s no longer a sacrifice. Temple service has to be done by priests. But now it’s no longer a sacrifice, there’s no more sacrificial service, so it can also be done by an appointed man, an ordinary non-priest. True, afterward the Mishnah says that he sends word to the high priest: “My lord the high priest, I have carried out your mission.” It seems that he does it as the agent of the high priest, so maybe it is still part of the sacrificial service and he does it as the priest’s agent. It’s still strange, but maybe. But here it is already clearer that the goat is no longer a sacrifice—though not yet completely clear. Already here I’ll note that some of the medieval authorities claim that the sending itself is not indispensable at all. Very strange. After all, we made all the preparations in order to send the goat to Azazel. The sent-away goat—that’s what it’s called. Meaning, you do everything, the lot, the confession, the laying on of hands, the tying of the crimson thread, and now it’s ready to be sent away. Now can you just go home? The sending is not indispensable—you don’t have to send it away? I don’t understand. All the preparations were made so that we would have a sent-away goat, and in the end we don’t send it away? It isn’t indispensable. If you want, send it; if not, don’t. That’s very strange. It’s a dispute among the medieval authorities, but some of them claim that the sending is not indispensable at all. Along the way the appointed man eats and drinks, and even violates the boundary restrictions. As far as he’s concerned, Yom Kippur is nothing—it’s an ordinary weekday. More than that: the Mishnah says they set up booths along the route, and they would pull at the goat’s hair. Now that is forbidden both in terms of Yom Kippur prohibitions and in terms of misuse of consecrated property. One may not do such a thing to a sacrifice. So here it’s already clear that it’s not a sacrifice. But not only is it not a sacrifice—what is happening around it is already no longer Yom Kippur. It’s an ordinary weekday. The appointed man eats and drinks, people violate prohibitions of labor by pulling at its hair. Meaning somehow Yom Kippur has been canceled, the sanctity of the sacrifice has been canceled—something here becomes very strange. In the end he reaches the cliff, and then they push the goat from the top of the cliff down below. It is explicitly stated in the Talmud that the pushing is not indispensable. Regarding the sending itself, it’s a dispute among medieval authorities. The pushing from the cliff—the Talmud explicitly says that is not indispensable. So if the pushing was not done, the commandment of sending still took place. On the face of it, that is super strange. All the preparations were made in order to send it to the cliff, and then at the cliff to push it. That is supposedly the climax, the goal. It’s a kind of crescendo that appears at the end of the process. No, no—the whole end of the process is just theatrical. According to some medieval authorities the sending is not indispensable; the pushing, according to all views, is not indispensable—the Talmud says so. So why did we do the whole process? The whole process is designed to get there. Something here is extremely strange. After the push from the top of the cliff, the next stage is that the limbs of the goat—usually they are smashed, because it falls from a very great height—may be used for benefit. Talmud, Yoma 67. That means there’s no sacrifice here, no anything, no sanctity. You may benefit from them, you may eat them, do what you want with them—bon appétit. No priest, no nothing. Meaning anyone who wants, the appointed man can make himself a meal there after he’s finished the job. Rabbi Yitzhak Ze’ev of Brisk, what is called the Griz, on Yoma 61, argues that if the goat remains alive after the push, one may slaughter and eat it—not only the limbs. And some commentators even permitted eating it without slaughter. Meaning, it is removed from Jewish law altogether, not just from Yom Kippur and from the sanctity of a sacrifice. There is something very strange here. Meaning, this thing reminds one of—

[Speaker B] How can that be? What? How can it be so degraded, that it’s already beyond Jewish law and beyond sacrifice and beyond sacrificial service?

[Rabbi Michael Abraham] Explanations—I’m describing the facts for now. Explanations in a moment. So I just want to remind you of Lewis Carroll, Alice in Wonderland—well, Alice in Wonderland, yes? It begins with her sitting on the riverbank and falling asleep. Then all the cards and the Mad Hatter and the rabbit and the queen and all the chaos, and at the end she wakes up and the whole story was a dream. Nothing existed. She went through hair-raising adventures, and then she wakes up and the whole story was simply fiction. It never happened. The feeling in the process I have described here is exactly the same. This is the peak of Yom Kippur. Everyone is gripped by trembling and awe. The sent-away goat atones for all the sins of the people of Israel. And this is the climax of the day. Okay? They make all the preparations in holiness and purity and wait for the moment when it will be pushed from the cliff, and then the crimson thread will tell us whether or not we have been atoned for. You don’t need to do it at all. It’s all nonsense. You’re dreaming. You dreamed the whole story. Nothing happened. According to some of the medieval authorities you don’t need to send it away, according to all views the pushing is not indispensable—the Talmud says this—and afterward you can just eat it. Just take some lamb, have a campfire and eat it. Nothing happened. Meaning, from the tremendous tension in which you were, suddenly you wake up and the whole story was a dream. Really Alice in Wonderland. What is the meaning of this strange process? So I want to claim—yes? How does the sanctity disappear? How does the sanctity disappear? The sanctity of a sacrifice—and at some stage the sacrifice evaporates. There are different stages; there is a dispute among the commentators exactly when this happens. But in the end, in the end, it is not a sacrifice. And all the medieval authorities I brought earlier, and the Guide for the Perplexed that Kotski mentioned before, join them. That doesn’t contradict what we saw before. They are simply talking about the final result—that at the end of the process it is not a sacrifice. But at the beginning it has sacrificial sanctity. Even after it has already been designated for Azazel—not only because before then you still don’t know which is for Azazel and which goes inside—but even once we already know which is for Azazel and which goes inside, both still have the sanctity of a sacrifice. And in the end it suddenly evaporates. Now the Talmud in Nedarim 29 says that bodily sanctity does not simply lapse on its own. Meaning, if something is sacred with bodily sanctity—what? I can’t hear. If something is sacred with bodily sanctity, then in order to remove the sanctity you have to do an act. Now here we didn’t do anything; on the contrary, the act done at the end—the pushing from the cliff or the sending—isn’t indispensable at all. And yet the goat becomes permitted. Meaning no act was done and the sanctity evaporated. It just went away. That runs against all halakhic logic. Halakhic logic says that bodily sanctity is the most stable thing there is. Only an act can remove bodily sanctity. It doesn’t just expire by itself. Okay? Now the question is how we explain this strange picture I’ve described here. So in order to explain this, and there’s really not much time left but I’ll at least begin, I want to make the following claim. In the kabbalistic world we speak about the sefirot. And the first two sefirot are wisdom and understanding. What is the difference between them? Understanding means understanding one thing from another. In more modern language: logic. Deriving a conclusion from premises. Understanding is logic. What is wisdom? Wisdom is—I think, I don’t remember whether the Ari says this or whether kabbalists explain it this way—כוח מה, the “power of what.” What does that mean? It is something that is true by virtue of itself; it does not draw from something else. In other words, its force is within itself. In other words, these are the first assumptions. Wisdom is what gives us the first assumptions; understanding draws conclusions from them, and the result is knowledge. And this whole system of wisdom plus understanding is what is called knowledge, okay? But for knowledge you need the assumptions that intuition gives us—we return now to what we spoke about at the beginning—and the logic, or rules of inference, that give us the conclusions from the premises. If we have that whole story, then we have a certain domain of knowledge, a certain field of knowledge, which is the concept of knowledge. Yes? Knowledge is the result of applying understanding to wisdom. Wisdom, understanding, and knowledge are the first three sefirot. Now, understanding also serves us in another context. Maybe we’ll see whether it’s another context. We know that there are fifty gates of understanding, right? Fifty gates of understanding, and corresponding to them gates of impurity—fifty gates of impurity. And in the New Zohar it is written in a midrash that when the children of Israel were in Egypt, the Holy One, blessed be He, took them out before the four hundred years of enslavement were complete, after only two hundred and ten, because there was concern that if they delayed any longer they would sink into the fiftieth gate of impurity and then they would no longer be able to get out. Okay? Those are the data. Now look at some interesting sources. There is a verse in Proverbs that says as follows—and what I am saying now is basically taken from Leshem, Leshem Shevo Ve’Achlama, the grandfather of Rabbi Elyashiv. He was considered perhaps the greatest of the Ashkenazic kabbalists, and he was in contact with Rav Kook, a bit older than Rav Kook. So it says: כל פעל ה’ למענהו וגם רשע ליום רעה—“The Lord has made everything for His purpose, and even the wicked for the day of evil.” A verse in Proverbs. So the Vilna Gaon writes as follows: ואמר כל פעל השם וגומר, וגם רשע וגומר, כי חמישים שערי בינה נבראו בעולם. ושער החמישים לא נתגלה עד ביאת הגואל, שהוא סוד עלמא דחירות. והיינו כי לסיטרא אחרא אינו רק מ”ט שערי טומאה ושער החמישים אין לו. וכאשר יתמלא כל המ”ט שלו אז יתבער הוא מן העולם, כי יבער כאשר יבער הגלל עד תומו. ולכן יתגלה שער החמישים ויתבער הוא מן העולם. Meaning: fifty gates of understanding were created in the world. And the fiftieth gate will not be revealed until the coming of the redeemer; that is the secret of the world of freedom. Because the other side has only forty-nine gates of impurity, and it has no fiftieth gate. And when all its forty-nine are filled, then it will be removed from the world. And therefore the fiftieth gate will be revealed and it will be removed from the world. וזהו כל פעל וגומר הוא נ’ שערי בינה, וגם רשע גימטריה הוא מ”ט שערי טומאה ליום רעה—“The Lord has made everything” equals fifty gates of understanding, and “and even” numerically equals forty-nine, the gates of impurity, “the wicked for the day of evil.” כי יפרוחו רשעים וכולי להישמדם—when the wicked flourish, it is in order that they be destroyed. כל פעל ה’ למענהו—“everything” numerically is fifty. “The Lord has made everything for His purpose” is fifty gates of understanding, the positive side. And וגם numerically is forty-nine—that is the gates of impurity, “the wicked for the day of evil.” So “The Lord has made everything for His purpose” is fifty gates of understanding, and “and even” is forty-nine gates of impurity. Meaning, there are basically fifty gates of understanding and forty-nine gates of impurity. And even among the fifty gates of understanding, the fiftieth gate is something a bit different. Now Rabbi Elyashiv, in the book HaDe’ah, Drushei Olam HaTohu, writes as follows: regarding the fiftieth gate of the gates of impurity—even though the Ramak also mentioned it in Pardes Rimonim, Gate of Gates, chapter 1—still, the Vilna Gaon in Proverbs on the verse “The Lord has made everything for His purpose” said there that the other side has only forty-nine gates of impurity, and no fiftieth gate. And when all its forty-nine are filled, then it is removed from the world. And that is what we said: for if they had remained slaves to Pharaoh any longer, they would have had no remedy, Heaven forbid, and would have been lost, because they had already entered the forty-ninth gate and stood there. And if that entire gate had been filled, they would have been lost, Heaven forbid. So in any case, the other side has no fiftieth gate at all; and even with the forty-ninth at full measure it also cannot exist at all. So make up your minds—is there a fiftieth gate of impurity? After all, they say that if they had remained in Egypt they would have entered the fiftieth gate of impurity and would have disappeared. But the Vilna Gaon said there are only forty-nine gates of impurity. There are fifty gates of understanding. That means—אך האמת ניתן לכתוב כי נראה עיקר כהגר”א, שאין בסיטרא אחרא שער חמישים כלל. והגם כי זה לעומת זה עשה אלוהים, ושערי בינה הם כנגד שערי טומאה, אז לכאורה היה צריך להיות אותו דבר, אך הוא רק עד מ”ט לבד. And these are the forty-nine arguments for purity and forty-nine arguments for impurity—yes, this is what the Talmud says, that one must show forty-nine aspects of purity and forty-nine aspects of impurity for every question. So forty-nine arguments for purity are forty-nine gates of understanding, forty-nine arguments for impurity are forty-nine gates of impurity. But the fiftieth gate—הנה הוא בבחינת אינסוף—it is in the aspect of infinity, as written in the Tikkunim, Tikkun 72, near its end. And the other side has no corresponding aspect at all, Heaven forbid, as the Ari wrote in Sha’ar HaKelippot chapter 3 in Etz Chaim. So Rabbi Elyashiv basically asks on the Vilna Gaon. Right? In the midrash, in the New Zohar, it says that if Israel had remained in Egypt, they would have fallen into the fiftieth gate, the fiftieth gate of impurity, and would not have managed to get out. But the Vilna Gaon said there is no fiftieth gate of impurity. Only on the side of understanding are there fifty. All right? So that’s one question. A second question: after all, this is not symmetrical. If there are fifty gates of understanding, there ought to be fifty gates of impurity. Right? So how can that be? Third, I want to add: why is it that what stands opposite the gates of understanding is the gates of impurity? Why not the gates of stupidity? What is the opposite of understanding? The opposite of understanding is impurity? The opposite of understanding is stupidity. It’s a bit like the wise son and opposite him the wicked son, not the foolish son. Yes? There too the Haggadah presents something that is not obvious on its face. So those are basically the three questions. I want to begin the line of thought for the answer—I see I won’t have time to finish it—but I’ll begin. Let’s take a moment to look at the concept of a gate. Gates of understanding, gates of impurity. What is a gate? A gate is something that leads from place to place. Right? That’s a gate. So let’s say there are rooms and gates connecting the rooms. The room is the place, and the gate is the thing that moves me from room to room. Okay? Now, if there are fifty gates of understanding, why are they called gates? That makes sense. Because understanding means understanding one thing from another. It transfers me from a premise to a conclusion. Right? So if the claims themselves are rooms, understanding moves me from room to room, from claim to claim. Okay? So basically wisdom is rooms and understanding is the gates. Okay? That is why this metaphor of a gate is used when we talk about gates of understanding. Because what they are saying is that understanding is the ways of deriving one thing from another. Okay? Or moving from one room to another—there is a gate that moves me from this room to that room. Okay? Now, the purpose of moving through gates is of course to arrive somewhere, at some room. Okay? Now, how do we interpret this structure of forty-nine gates of understanding? Or gates of impurity—forty-nine gates of understanding, forty-nine gates. How many rooms are there there? What do you think? Let’s say a chain of forty-nine gates of understanding. How many rooms are there? Room-gate, room-gate, room-gate, right?

[Speaker C] It should be fifty. Minus one. Why minus one? Plus one.

[Rabbi Michael Abraham] Fifty rooms, right? Room-gate, room-gate, room-gate.

[Speaker C] Because it ends in a room.

[Rabbi Michael Abraham] Yes.

[Speaker B] But you need a gate to enter the first one too. That’s it.

[Rabbi Michael Abraham] That’s all if we’re talking about a linear chain. But if the conditions of the language are circular—if we close the end of the chain back to its beginning—how many rooms are there?

[Speaker C] One less.

[Rabbi Michael Abraham] Forty-nine, right? Room-gate, room-gate, room-gate, and back again. Meaning, it closes on itself. So a circular chain is forty-nine gates and forty-nine rooms. A straight chain is fifty rooms connected by forty-nine gates. Okay? Those are the two possibilities; there aren’t any others. So what does that actually mean? Try to see what it means, and I’ll spell it out more next time. What this basically means is as follows: if the rooms are wisdom and understanding is the gates—or logic—and the rooms are wisdom, that is, the premises or claims, and understanding is the logic. Think, for example, about the axioms of geometry. We begin from them. Now I apply a logical rule, which is a gate of understanding, and I create another proposition, I prove a theorem. Right? Finished—a room; it’s a claim. Now from that theorem I use logical tools and prove another theorem. So that too is a room. So the gates of understanding basically describe the intellectual process. We begin from a room that is wisdom, and with the tools of understanding, with logic, we derive more rooms and more rooms and create a kind of chain like that. Except that one can close it either circularly and we return to the first room, or linearly and we arrive at some room from which there is no exit. There is a first room to which no gate leads, and there is a last room from which no gate goes out. Okay? What is the difference when we use this as a metaphor for forms of thought? How would you interpret these two structures? I’ll tell you how. The circular structure is basically a structure that accepts only logic as something valid. There is no room without a gate leading to it. There is no claim—I’m not willing to accept a claim if I have no proof that proves it, if there is no understanding deriving that claim. I do not accept that claim. So how is a logical chain built in such an approach? It only says: if this is true then this is true, and if this is true then this is true. But none of those things is true in itself. Because if you think about geometry, if the axioms of geometry seem arbitrary to me because I have no proof for them, then the theorems I proved on their basis are also arbitrary, because they were proved on the basis of arbitrary axioms, right? So the whole structure of geometry is an arbitrary structure. I’m not really learning anything. I can’t say that the sum of the angles in a triangle is one hundred and eighty degrees. All I can say is that if you adopt these assumptions, these axioms, then the sum of the angles in a triangle is one hundred and eighty degrees. But if I ask you what the sum of the angles in a triangle is, you are supposed to answer me: I don’t know. It depends on your assumptions. And which assumptions are correct? I don’t know. Draw lots, make something up, whatever—you have no correct assumptions. You understand that the metaphor describing such a thing is basically a circle. Because what does that mean? There is no room that begins the process. Because every room—think about the linear process. In the linear process we begin from a room that is not created by, not reached by, a gate. It is a room that begins the process. That is an axiom. I have no proof leading to it. It is an axiom. From it, gates begin leading me to more rooms. A kind of initial assumption. An initial assumption. If as far as the existence of the first room is concerned I am unwilling to accept the existence of a room to which no gate leads, then I am basically living in a circular world, right? Because in a circular world there are only rooms that have gates. Then I have only forty-nine rooms. I do not recognize the existence of the fiftieth room. The fiftieth room—or really the first room, not the fiftieth. The first room is a room to which no gate leads, and I do not recognize it as a room. Therefore the circular process is basically a skeptical process. It is the process that says I am not willing to accept axioms, not willing to accept claims for which I have no proof. I accept only things for which I have proof. But we’ve already seen that someone who accepts only things he has proof for cannot accept anything. Because the axioms on which he would build the proof he cannot accept, because they themselves have no proof. Then the whole structure is unacceptable to him, and so he goes around chasing his own tail. All he can say is that if this is true then this is true, and if this is true then this is true, and if this is true then this is true. All he can say is that there is consistency in the system. He cannot say of anything that it is true. That is the circular metaphor. The linear metaphor says this: the axioms are true because my intuition tells me they are true. I have no proof for them, there is no gate leading to this room. But this is the first room. From it I set out—that is wisdom, the power of what. From here understanding begins deriving more and more conclusions, more and more rooms, another gate of understanding, another room, another gate of understanding, another room, and so on. All the theorems we derive from axioms. If I trust the axioms, then I trust all the rooms I built on the basis of the axioms. Meaning, as far as I’m concerned, all fifty rooms are rooms. They taught me something. As far as I’m concerned, the sum of the angles in a triangle is one hundred and eighty degrees. It’s not just an if-then; I know that the sum of the angles is one hundred and eighty degrees. Because I accept the axioms. It’s not merely hypothetical that if the axioms are true then this is true. The axioms are true, and if this follows from the axioms then that too is true. So I’m looking at the same chain itself, but these are two different perspectives. The dispute between them begins with the question of how I relate to the first room. Is the first room acceptable even though there is no gate leading to it, or not? And that determines whether I am on a circle or on a straight line. Let’s stop here. We’ll continue next time. Any comments or questions?

[Speaker C] Everything the Rabbi just explained now about the gates and all that—that’s supposedly in order to answer about this sacrifice, right? To Azazel?

[Rabbi Michael Abraham] I’ve only laid the foundations, yes. I’ll come back to it.

[Speaker C] You laid an initial assumption, yes.

[Rabbi Michael Abraham] I’ll return to the questions I asked.

[Speaker C] Just a very, very side question, yes? Do we have to believe in the forty-nine gates of impurity?

[Rabbi Michael Abraham] Wait, wait—I haven’t yet explained what the forty-nine gates of impurity are. I’ll explain that—

[Speaker C] That later. I have another question before all that, before this, connected to artificial intelligence and the whole series.

[Rabbi Michael Abraham] You wanted to ask about artificial intelligence, yes.

[Speaker C] I wanted to ask: in the Rabbi’s opinion, can today’s computer, with AI and so on, solve the Poincaré conjecture?

[Rabbi Michael Abraham] How do you want me to answer that? Maybe yes, maybe no. We’ll wait. As a mathematician—

[Speaker C] I have no idea.

[Rabbi Michael Abraham] How should I know? There are already things it has solved; maybe it’ll solve more things. I have no idea. I have no way to answer that. I don’t think anyone can answer that question.

[Speaker C] In 2003 a computer couldn’t do what Perelman did.

[Rabbi Michael Abraham] Okay, true, true. But now they’re already saying that they can do things like that.

[Speaker C] Or the question is whether they really are doing it.

[Rabbi Michael Abraham] Or that the computer—two weeks ago, or something, three weeks, a month, something like that—there was a report that some artificial intelligence model, I think from Anthropic, or maybe GPT, I don’t remember anymore, solved some Erdős conjecture—how to arrange points on a lattice. Some problem there.

[Speaker C] When was that?

[Rabbi Michael Abraham] In the last month.

[Speaker C] Really? I didn’t see that. Wow, that’s interesting. Okay, I’ll look for it.

[Rabbi Michael Abraham] Fine. Again, we’ll come back to it and we’ll get to it. I first need to define artificial intelligence. In the end all these things will have meaning. These aren’t just nice remarks for the sake of nice remarks; they’ll have meaning for our discussions about artificial intelligence.

[Speaker C] God willing. That’s why we study, yes.

[Rabbi Michael Abraham] Rabbi—

[Speaker B] Rabbi, can I ask something from a different series? It’s connected, but to today. Okay. The Rabbi spoke this week in some lecture that was uploaded to the site about pluralism and monism and Beit Shammai and Beit Hillel. And I want to ask the Rabbi: if, as the Rabbi claims, the dispute—legal disputes—are rational disputes, rational, then I don’t understand what the Rabbi explained there, that supposedly Beit Shammai and Beit Hillel—why? Because they considered the arguments of the other side, listened to the reasoning, so they expanded their rational consideration and therefore maybe ruled like them. That doesn’t sound serious to me at all, because obviously if you want to begin a dispute at all, you’re supposed to examine all the data and all the considerations and all the reasoning, and only afterward decide. When in that state you listen to the other side, it’s simply part of forming an opinion. You do indeed have some initial opinion, but you can’t—no, no, but then it isn’t called that they “gave precedence.” It’s not even a dispute. Obviously both sides are supposed to—someone who isn’t willing to listen at all to other considerations is simply closed off; it’s irrelevant. No, one second, Rabbi. Therefore I say that this is more proof that the dispute cannot be a rational dispute, because obviously both sides, if they are serious people—Beit Shammai and Beit Hillel—considered both sides and all the reasoning. Afterward, when it comes to deciding among the reasons, that no longer belongs to rational considerations, and then it really does involve an emotional matter entirely; and then when you feel the other side—

[Rabbi Michael Abraham] I already see where this is going, and once again we’re returning to the same thing. You’re again assuming a binary: either people listen or they don’t listen. Very often in discussions—you can see this today too—both sides listen to one another politely, but they don’t really listen. They don’t seriously weigh the other side’s words. The difference between Beit Hillel and Beit Shammai is that both of them probably heard what the other said, but Beit Hillel seriously considered it before forming a position. Beit Shammai only looked for answers to explain to Beit Hillel why they were wrong. We know such things from arguments we know today too. Therefore it’s not zero or one—these listened and those didn’t listen—but rather the question is how seriously you take the other side’s considerations into account when you form a position. Beit Hillel did this in complete seriousness, and Beit Shammai probably were more casual about it. Well, that—

[Speaker B] sounds serious—

[Rabbi Michael Abraham] They were, because they were sharper.

[Speaker B] It almost sounds unnecessary to say that Jewish law is ruled like Beit Hillel; it follows automatically. If there is one side that listens to the other and one side that doesn’t at all—

[Rabbi Michael Abraham] No, but Beit Shammai were sharper.

[Speaker B] Fine, but when you form a position, a mature person has to examine all the arguments; otherwise he’s not serious at all.

[Rabbi Michael Abraham] And that is far from trivial. If you have the opinion of a very smart person and the opinion of a less smart person, but the less smart person listened to the smart person and the smart person pays no attention to the less smart person—is it so obvious to you that the law should be ruled like the less smart person?

[Speaker B] No, I don’t—

[Rabbi Michael Abraham] I didn’t say it was obvious. In this case it simply isn’t trivial.

[Speaker B] But I would expect two serious people at a minimum, before they form a position—

[Rabbi Michael Abraham] I would expect that too. But all of us, I think—even if we are serious people—all of us sin in this, because we also have ego, and we do not always listen to the other side or weigh all the arguments seriously.

[Speaker B] Since the main problem is not really dispute. If I were meeting Ben-Gvir—no, I think the Rabbi—I don’t know, for example, forget the Rabbi. If I have a dispute with Ben-Gvir and Smotrich, it’s not that he’ll tell me some historical or factual thing I don’t know, or that he doesn’t know. That would be minor. I’ll listen to him in order to know the facts. It’s obvious to both of us that the dispute between us is much deeper than facts of reality.

[Rabbi Michael Abraham] Not facts—there are also non-factual considerations.

[Speaker B] So considerations rooted in the world of emotion and intuition. Fine, let’s move on together.

[Rabbi Michael Abraham] And who said that isn’t—again we’ve returned to the same point. Fine.

[Speaker C] By the way, even today there are such things, that some halakhic decisors rule Jewish law while not taking other decisors into account at all. Even today there is that.

[Rabbi Michael Abraham] Same issue, same issue.

[Speaker C] Yes. For example, this week I had an argument with someone about umbrellas on the Sabbath. As of today it has been accepted by the whole public that it’s forbidden—but there are many decisors who hold that it is permitted from the outset. Yes, correct. There are also discussions by Yoel about it, and because of the Chazon Ish, out of respect for the Rabbi—

[Rabbi Michael Abraham] There is a pamphlet by Tiferet Yisrael about umbrellas, yes.

[Speaker C] Yes—no—because of respect for the Chazon Ish, none of us use umbrellas on the Sabbath. It’s a bit absurd, but that’s the reality.

[Rabbi Michael Abraham] Fine, okay.

[Speaker C] All right, friends, Sabbath peace. Have a good month. A good and blessed month.

[Rabbi Michael Abraham] Goodbye.