Lecture dated 12 Tammuz 5767

[Rabbi Michael Abraham] It is written: “And Moses said: About midnight I will go out into the midst of Egypt.” And in Exodus, in another parallel verse, it says: “And it was at midnight, and God struck every firstborn in the land of Egypt, from the firstborn of Pharaoh who sat on his throne to the firstborn of the captive who was in the dungeon, and every firstborn of cattle.” Above it says “about midnight,” and here it says “at midnight.” What’s the difference? Why here is it with a bet and there with a kaf?

[Speaker B] There it’s Moses, and here it’s God.

[Rabbi Michael Abraham] So the Mekhilta says: Why was “And it was at midnight” stated? Because it says, “And Moses said, so said God: About midnight I go out,” and so on—because it is impossible for flesh and blood to determine the exact midpoint of the night, but here its Creator divided it. Rabbi Yehudah ben Beteira says: The One who knows its hours and its seasons divided it. In any case, the Holy One, blessed be He, Himself knows exactly when the midpoint of the night is, and therefore says “at midnight.” The Holy One, blessed be He, knows when that is; Moses our rabbi cannot know such a thing. That’s in the Mekhilta of Rabbi Shimon bar Yochai. But when Moses said it to Pharaoh, what did he say? “So said God: about midnight,” and so on. He said to him: the matter stands balanced for when the night is split, whether by a hair’s breadth above or by a hair’s breadth below, one who sits over a sundial and aligns the hour to a hair’s breadth, for no kingdom touches another even by the width of a thread. Rather, when the time comes for a kingdom to fall—if by day, it falls by day; if by night, it falls by night. “Sundial” means a sun clock.

[Speaker C] A sundial, yes, a sun clock. But at night?

[Speaker B] What does that have to do with the night? What does that have to do with the issue of the instant?

[Rabbi Michael Abraham] One second, I’ll come back to that in a moment. In short, what we have here in the Mekhilta—mainly in the Mekhilta of Rabbi Shimon bar Yochai, and I think in the Mekhilta of Rabbi Yishmael too—is really very clear: it’s talking about an actual mathematical instant, right? They speak there of a hair’s breadth: up to it this kingdom, from it onward another kingdom. Meaning, there is some transition here between states that is itself really a point of division.

[Speaker D] The transition could be some kind of line, not something discrete.

[Rabbi Michael Abraham] No, no—about the discrete and the continuous we’ll talk later. The Talmud in Berakhot 3a speaks about King David, who got up at midnight to play music and engage in Torah, so it brings the following. “And did David know when half the night was?” How did King David know when midnight was? “Now Moses our rabbi did not know, as it is written: ‘About midnight I go out into the midst of Egypt’”—that’s a hint to the Mekhilta we just read. When it says “about midnight,” you see that Moses did not know the exact midnight; only the Holy One, blessed be He, knows.

[Speaker D] Moses said not that he himself would go out, but that the Holy One, blessed be He—yes, but when Moses says it, then he doesn’t know. Why? Moses says: the One who knows when midnight is—

[Speaker B] At midnight He will go out.

[Rabbi Michael Abraham] Fine. When Moses speaks, Moses doesn’t know; and those to whom Moses is speaking are also human beings.

[Speaker B] Maybe Moses is worried that if there’s a delay—

[Rabbi Michael Abraham] So Moses says “about midnight.” You should know—Moses says this to Pharaoh, and it’s as if if Pharaoh makes a mistake, then he’ll say that the Holy One, blessed be He, is a liar, let’s say.

[Speaker B] Rashi says that in the midrash, Rashi, right. In any case, what this comes to teach is that there is—

[Rabbi Michael Abraham] A difference between the knowledge of the Holy One, blessed be He, and the knowledge of Moses our rabbi. Never mind that at the moment, because seemingly the Holy One, blessed be He, is also speaking to human beings, so that may indeed be the explanation Yitzhak gave here. In any case, the conclusion is that Moses really does not know when midnight is, and David does. The Talmud says: “If you say that the Holy One, blessed be He, said to him ‘about midnight’—is there uncertainty before Heaven? Rather, He said to him, ‘tomorrow at midnight,’ and he came and said ‘about midnight’; evidently it was uncertain to him.” So you see that Moses our rabbi was unsure about it. The Talmud asks: “And did David know?” That’s where the whole question ends—yes, it’s a long passage that is all one question—“And did David know?” So the Talmud says: David had a sign. As Rav Acha bar Bizna said in the name of Rabbi Shimon Hasida: A harp would hang above David’s bed, and once midnight arrived, a north wind would come and blow on it, and it would play on its own. Immediately he would rise and engage in Torah until dawn broke. So he had some sign from Heaven.

[Speaker C] And that’s the meteorology of the Land of Israel. If you notice, for example, even on hot days like today, in the morning hours there’s a western wind, toward dawn an eastern wind. Right. And that isn’t very precise in time. Apparently that switch wasn’t exact. No, no, I’m talking about meteorology that I know. With David maybe—maybe in his case it was a specific time, I think it happened at midnight. What is midnight? He knew where to place the harp so that exactly when the wind came at midnight… But that can’t be, because it’s not really exact, not really to a hair’s breadth; it doesn’t switch by a hair’s breadth. Right. Therefore I don’t think this is a meteorological phenomenon. Yes, but it is interesting. In any case. Yes. Okay.

[Rabbi Michael Abraham] Maybe for King David the Holy One, blessed be He, arranged that in his period this transition would always happen exactly at midnight. For us, in ordinary times, it happens more or less. Yes, on a day like today, with the heat wave, everything gets messed up.

[Speaker B] Fine.

[Rabbi Michael Abraham] In any case, later in the Talmud we’ll see another opinion, that Moses our rabbi also knew, and there is a parallel midrash on that, but that’s not important right now—look on the page. There is a sharp point here that I always knew in the name of the Brisker Rav, but I looked and couldn’t find anywhere that he says it. I tried to investigate a bit, and some Jew from Bnei Brak found the source for me. The source is actually not the Brisker Rav, but someone who brought many things in his name—though this one he does not bring in his name. He brings it in his own name: Rabbi Diskin. He wrote Ohel Yehoshua, the book Ohel Yehoshua. So he brings an interpretation of the second verse we mentioned there, the verse about midnight. “One may note that you cannot really find such a time as midnight, for when one divides the night into two, the first half is before midnight and the second half is after midnight. But midnight itself occupies no time at all and has no reality at all, for it is only a name for the division of the night. For any time that is in the middle—even if it is divided into two—half of it is here and half of it is there. If so, how can midnight be found?” And what is midnight? Midnight is not a time in itself. The time up to it is before midnight, and from it onward is after midnight. But midnight itself obviously cannot have any length, because if it had any length, then we would split it too in the middle, and what comes after it would be after midnight and what comes before it would be before midnight. So clearly, in the end, after all the halvings, midnight itself has no length at all. It’s a single instant. There really is no such thing as midnight. After all, midnight is a boundary that cuts two parts of a line, but it has no measure of its own. So what exactly was he trying to ask? He meant to ask: what are you telling me—that Moses our rabbi didn’t know, but the Holy One, blessed be He, did know? The Holy One, blessed be He, also can’t know such a thing. There is no such instant. That’s the point. He says this is not a problem of lack of knowledge. If earlier in the Talmud we read that this is one fifty-eight-thousandth of an instant—there they weren’t talking about the instant of midnight but the instant when the Holy One, blessed be He, is angry—but the main point is the grasp of an instant in time. There the conception is that an instant is some very tiny duration. So clearly, in principle, it could be known. The Holy One, blessed be He, knows when it is; we don’t know. How do we know exactly when the Holy One, blessed be He, gets angry? We don’t. But where we are dealing with something that has no reality at all on the time axis, like midnight, then it makes no sense to say that we do not know and the Holy One, blessed be He, does know. There is nothing there to know. There is no such instant. There is no midnight. There is before midnight and after midnight; midnight itself is not a time at all. It cannot be known. That’s his question. That’s what he means to ask. Now look at what he answers, the second half. I always liked this point. So he says as follows: “It seems simple, for likewise one may ask: what was there at midnight? ‘At midnight I will go out and I will strike every firstborn,’ right? This was the death of the firstborn.” So he says: “It seems simple, for likewise one may note that death too is not a matter of time. Death too is not something that happens in time. Why? For beforehand he was alive, and now he is dead. It thus follows that there is no time of death at all.” There is no instant at which he dies. There is a time when he is alive, and after that there is a time when he is dead. The transition between the state in which he is alive and the state in which he is dead is sort of called the moment of death, but there is no such thing. Death is a state; it is not a transition. The transition itself never happens at some time; there is no instant in which the transition occurs. You are alive until here, and from here onward you are dead.

[Speaker B] You can’t—

[Rabbi Michael Abraham] Point to it; there is no instant in which the transition happens. So he says: “For so long as he has not yet died, he is alive, and once he has ceased to live, he is dead. It follows that there is no time of death at all.” That’s what he says. Death too has no time. And now, look, everything is resolved. Why? “And indeed this is certainly true.” It really is true. “Therefore the first question is settled”—the first question he asked above. Why? “For thus it was in the plague of the firstborn: they were alive in the first midnight, and in the second midnight they had already ceased to live and were dead. And likewise, just as midnight is not a time, so too the time of death is not a matter of time; rather, this itself—that the transition from death to life was equal to the transition from the first midnight to the second midnight—and this is ‘And it was at midnight,’ meaning not the time of midnight, because there is no such time, but rather that midnight, just as half the night divided between death and life of the firstborn of Egypt…” What is he really saying? He is basically saying this: correct, there is no instant of midnight, but there is also no instant of death. What happened to the firstborn of Egypt? They lived until a certain point, and from then onward they became dead. So that transition is exactly at the instant when the night transitions from the first half to the second half. Just as there is no instant that is itself called midnight, there is also no instant in which the firstborn of Egypt die. It is simply a transition between two states, and that transition happens simultaneously. So really there is no need to arrive at some instant of midnight; there is no instant of midnight. Fine. Now, the instant in which, for example, the Holy One, blessed be He, is angry—it will be hard to say such a thing about that, because that is not a transition. The Holy One, blessed be He, is angry for an instant. There, there you won’t be able to say such a thing.

[Speaker D] The question is whether the analogy—the example he gives there of the transition from life to death—is really a principled example, or whether more deeply you could say that every human activity is made up of some sequence of—

[Rabbi Michael Abraham] Events.

[Speaker D] And changes, and in the end, about each one of them you can’t say exactly when—

[Speaker C] It happened.

[Rabbi Michael Abraham] Exactly, exactly, right—

[Speaker C] Look, for example, at the Holy One, blessed be He, being angry, like the heap paradox. Fine, there is some state of dying. We all know: the last heartbeat, the last three tiny spurts of blood that came out of the heart—is that alive or dead? Clearly he assumes this is an intermediate state, meaning life and death are intermediate states.

[Speaker B] Yes, that’s the dispute: whether human beings merely perceive things that way, or whether there are objective truths.

[Speaker C] I don’t know—you don’t know. You simply don’t know. There is a Jewish law definition of death, from when one is allowed to say—

[Speaker D] It doesn’t—

[Speaker B] Matter, but the Jewish law definition, the definition—

[Speaker C] The Jewish law definition is: if breath ceased from the nose and he is not breathing, then what about the very last bit of air that came out of the nose—is that alive or dead? The Christian—

[Rabbi Michael Abraham] No—

[Speaker B] So that’s a good comment. That’s only from our perspective as human beings.

[Rabbi Michael Abraham] No, fine, but—

[Speaker B] He says even the Holy One, blessed be He, does not know when the transition is.

[Rabbi Michael Abraham] He says no, not because the Holy One, blessed be He, knows when—it’s like the heap paradox, which we’ve brought up several times.

[Speaker B] But that’s us again.

[Rabbi Michael Abraham] No, also the Holy One, blessed be He.

[Speaker B] The last tiny bit—whether it’s alive or dead—the heap paradox—

[Rabbi Michael Abraham] The heap paradox is something that even the Holy One, blessed be He, has a problem with. What here—

[Speaker B] What’s the difference?

[Rabbi Michael Abraham] No, the heap paradox does not point to inability. The heap paradox says that there simply is not, exactly, a definition. So it has nothing to do with the Holy One, blessed be He.

[Speaker B] So what he’s claiming is: there is a heap paradox here?

[Rabbi Michael Abraham] Because even in death you can define it such that the transition between death and life is not a jump from one to zero. It is a transition from one that decreases continuously to zero, on a sort of slope, and then when do you define him as having ceased to live and begun to die? There are states of three-quarters alive and one-quarter dead, half-and-half, one-quarter alive and three-quarters dead, and so on.

[Speaker B] But that’s us as human beings.

[Rabbi Michael Abraham] No, no, no.

[Speaker C] I’m saying—I saw the monitor of my aunt, my uncle’s wife, while she was dying, and the heartbeat rate, this sinus graph, it goes—it’s not sudden, it gets more and more moderate. Now, below a certain amplitude, when the normal amplitude is like this on the screen, taking up the whole screen, and then… so is that alive or dead?

[Speaker B] Definition.

[Rabbi Michael Abraham] Okay, but that is exactly the point: there is some definition here that is a bit arbitrary. It is not a state of—this is not a state of alive and dead in a sharply distinguished way. There is a continuum of states here. Who doesn’t distinguish? Nobody. Even the Holy One, blessed be He, doesn’t. A doctor certainly doesn’t, because there is nothing here to distinguish—that is exactly the distinction I want to sharpen here. Meaning, if we are speaking about a very short instant, then okay—that is only a human limitation. We cannot detect it, define it; the Holy One, blessed be He, can. We are talking about another kind of situation: it may be that there is nothing there to distinguish at all—not that we cannot; there is nothing there to distinguish. Can the Holy One, blessed be He, tell you when something is a heap? No. The concept itself is undefined. It’s not because of inability, it’s not that the Holy One, blessed be He, doesn’t know, but that the concept itself is undefined. So it’s not—you understand? It’s not that the Holy One, blessed be He, can’t do something, but rather there isn’t—also for me the problem is not that I can’t; rather there is no such thing.

[Speaker D] The comparison between a heap and life and death seems to me not necessary. A heap is a concept that—

[Rabbi Michael Abraham] Right, there is room to say that—

[Speaker D] Has a certain convenience, but really there’s not all that much importance to the definition, so it’s a kind of everyday concept. Right. Whereas life—it may be that we are trying to define it as death and life, and maybe for the Holy One, blessed be He, there really is—I don’t know—perhaps at that moment when the soul is taken, for example. Maybe not; possibly.

[Rabbi Michael Abraham] I’m saying I don’t know; the Holy One, blessed be He, knows—I don’t know. But is it necessary? Maybe yes and maybe no; I’m not sure. What Yossi raised is that there is also the possibility that essentially this does not exist, and then even the Holy One, blessed be He, cannot—maybe yes, maybe no, I don’t know. But Rabbi Diskin notes—Rabbi Diskin is basically assuming implicitly that the state of dead and alive is binary. Either alive or dead, that’s it. And maybe we don’t know the transition, but the Holy One, blessed be He, certainly does. It is not clear that this assumption is correct. So there is some assumption here. Fine, an assumption.

[Speaker B] So let’s assume a different assumption.

[Speaker C] Legitimate. And that also works with the verse: “And it was about midnight, and I killed every firstborn in the land of Egypt.”

[Speaker B] “I killed,” because “I killed” is—if you assume something else, the verse doesn’t work for you.

[Speaker C] No, I can simply say that the Holy One, blessed be He, is capable, in the end, of doing something we are not capable of doing: killing within a span of time—within what span of time?

[Speaker B] It doesn’t exist.

[Speaker C] One can move a person from alive to dead apparently in a time that doesn’t cross over midnight—without time.

[Speaker B] If it doesn’t exist, then it doesn’t exist.

[Speaker D] Meaning that in principle you cannot show that this was before and that was after.

[Speaker B] That’s what he is forced to say; he is forced to put in that assumption and say: that’s how it was.

[Rabbi Michael Abraham] No, that’s perfectly fine—legitimate.

[Speaker B] I’m saying that any other assumption will bring you to a problem.

[Rabbi Michael Abraham] It won’t bring you to a problem; it will only say that you cannot know, but the Holy One, blessed be He, can know. He says no: in principle this does not apply, and the Holy One, blessed be He, also doesn’t need to know anything here—it is only a transition. There really is no such instant that we are looking for; rather this is a transition from a state of life to a state of death. That transition happens exactly when the night also passes from the first half to the second half. They simply happen in parallel. So there is no event here that you need to place on some point in time. There is a transition here that you place alongside a transition of the time-axis itself, and therefore there is no problem even though there is no instant of midnight at all. Everything is fine.

[Speaker B] You place the two transitions, but you need to know when the first transition happens.

[Rabbi Michael Abraham] But there is no “when.” Really, it is not correct to define when it happens, because the transition itself has no time at which it happens.

[Speaker B] How do you align them exactly together?

[Rabbi Michael Abraham] I don’t know; the Holy One, blessed be He, knows how to align it.

[Speaker B] If He does in fact know in any case when and how to align—

[Rabbi Michael Abraham] If there is no such time, then He aligns the stretches of time whose boundary this divides between; He does not align an instant.

[Speaker B] Yes, but to align the—

[Rabbi Michael Abraham] Two transitions also takes time. Yes, but the time is that, say, He aligns the period of life of the firstborn so that it is exactly the first half of the night, and the period of death so that it is exactly the second half of the night; automatically the transition happens at the same time. But when He aligns it, He aligns what does take time, not what does not take time. Fine. In any case, the point here is really that he assumes that such a thing simply does not exist on the time-axis at all—these transitions, death, or the transition from the first half to the second half. If we take as an example the anger of the Holy One, blessed be He, there you won’t be able to say this. Because when we say that the Holy One, blessed be He, is angry at a certain instant in the day, that is a time.

[Speaker B] It happens—

[Rabbi Michael Abraham] At some point. It is not a transition between states; it is a state in itself. About that, you cannot say that it is not on the time-axis. Therefore, earlier the Talmud indeed assumed that time has some duration—one fifty-eight-thousandth. It does not say that this is a mathematical point in time. I said it may be that in the end they perhaps do reach the conclusion that it is a mathematical point in time, and maybe I’ll explain that in a moment. But at least on the face of it, it seems to fit very well. Midnight really is a single point, so Rabbi Diskin says that actually it is not even a single point—it does not exist at all on the time-axis. It only happens in parallel to the transition of the time-axis. But the killing itself is not a state; it is a transition between states. In contrast, the anger of the Holy One, blessed be He, is certainly a state, and a state always takes some amount of time. That is why the Talmud asks: how long is an instant? Like the time needed to say a word, one fifty-eight-thousandth, whatever—but it has some definite duration. So really there are two different discussions here. The first discussion is not dealing with an instant. When the Talmud asks how long an instant is, “instant” there does not mean what we mean here, namely a point in time, but rather a very short time. But the truth is that I think he is assuming something that should be examined a bit more. Let me perhaps preface this with an introduction. There are situations in which—let me start differently. We usually understand that when there is zero probability, zero chance that something will happen, then it is impossible. Not impossible—it’s zero chance. That’s not correct. It’s not correct because there are many situations in which things happen whose probability is zero. For example, someone makes a random draw to produce an integer. Out of all the integers, I choose one at random—one of the numbers, yes? What is the probability that nine will come out? Zero. One over infinity. There are infinitely many integers. The probability is zero, right? Yet if I make such a draw, some number will always come out. Right? Some number will come out. Meaning, in a draw of that kind, every result that comes out—I know with certainty in advance that whatever result comes out, it was an event whose probability was zero. Right? Meaning, when I say—saying that something has zero probability does not mean it is impossible. There are situations in which things definitely happen whose probabilities are—I don’t even need the infinity of integers, also all the numbers between zero and one, all the real numbers. I choose some point in the interval from zero to one at random; the probability of any point is zero, but still one point will always come out, right? In every lottery with infinitely many outcomes, and in a fair lottery, the probability of each one of the outcomes is zero. But in every such lottery one outcome will come out. Right? So clearly saying zero probability does not mean saying impossible.

[Speaker D] On the other hand, there are situations—and this is even a less good example—

[Speaker B] Because with real numbers—

[Speaker D] When something comes out, how can you even say what came out? In the end you make some finite truncation.

[Rabbi Michael Abraham] The moment you do that truncation—

[Speaker D] It becomes a finite number of—whereas with the natural numbers you really know what came out.

[Rabbi Michael Abraham] And there technically it would be hard to make such a lottery, because it would not have infinitely many outcomes. Okay. Also with integers, by the way, you can ask similar questions. Every actual mechanism of lottery you make among integers will never really—it will always have some threshold. And if you do it on a computer, for example, the number of bits will determine how far you can go. You really can’t do it on an infinite scale, right. But never mind. It’s not important. You cannot do it in a truly infinite way. It’s a thought experiment, yes, a thought experiment. Clearly, in a lottery of that type, something will come out whose probability is zero.

[Speaker D] And that’s the idea. And maybe it’s the other way around—maybe what that actually says is that since you cannot really define—

[Rabbi Michael Abraham] A mechanism.

[Speaker D] Of lottery with an outcome, a mechanism that really takes all the possibilities into account—so the moment you make a mechanism, it is a finite mechanism, and therefore not really what you wanted. Right.

[Rabbi Michael Abraham] But when you make a finite mechanism, the probability won’t be zero either. Right. Then we’re not even there. Never mind. But in this thought experiment there is an outcome that will occur even though its probability is zero. Meaning it is not an impossible outcome even though its probability is zero. Saying zero probability and saying impossible are not synonyms.

[Speaker C] Let’s say it takes an hour to carry out the draw, and the chance of getting the number nine is one in a billion on a real, practical computer, right? So that doesn’t mean that the chance of getting the digit nine is one in a million years; rather, once the draw has been made, the chance that getting the number nine will happen is one in a million years, but once the draw was carried out within the hour, some number came out. And that’s another expression of the same phenomenon.

[Rabbi Michael Abraham] That’s what the rabbi is saying. It’s the same idea, just in practice.

[Speaker C] Fine. It doesn’t mean that it won’t happen in the next minute.

[Rabbi Michael Abraham] No, that’s exactly the point.

[Speaker C] Even an event whose probability is one in a billion can still—

[Rabbi Michael Abraham] Happen, and it will always happen. In nine billion events, this event will happen to you, and you’ll say: oops, how can that be? It has a probability of one in nine billion. How can it be that it happened? That can’t happen. But I will tell you in advance: it is completely obvious that the event that happens here will be an event whose probability is one in nine billion. That I know in advance. So I don’t think this distinction is essential. In any case, let’s push this a bit further, the distinction between these two things. When we talk about an event that is impossible, we also say that its probability is zero, right? But there it is never the result of a calculation. That is a very subtle and important point.

[Speaker B] And there it will always really be zero. What? There it will always be zero.

[Rabbi Michael Abraham] What will always be zero?

[Speaker B] The impossible.

[Rabbi Michael Abraham] An impossible event has probability zero, but an event whose probability is zero is not always impossible. That’s the claim. And I’m saying this: there are two situations of zero probability, then, right? There’s a situation where the probability is zero but it’s possible, and there are situations where it’s zero probability because it’s impossible. What’s the difference between those two situations? The difference is that something whose probability is zero but is possible—that zero is the result of a statistical, probabilistic calculation. You simply see that there are infinitely many possible outcomes of a lottery, the probability of each outcome is one divided by the number of outcomes, so it’s zero. Right? I do a statistical calculation and the result is zero. When I do a statistical calculation and the result is zero, that means the event is possible with zero probability. When I speak about an event that is genuinely impossible, that is never the result of a statistical calculation. Never. There is no statistical calculation that tells me an event is impossible. And this is a mistake made by a great many people trying to prove things from all sorts of directions—pro faith, anti faith. I’ll bring an example in a moment. It’s always a definition that has nothing to do with statistics. For example, let’s say I think it’s impossible for that picture suddenly to disappear from the wall from one moment to the next and leave nothing behind. Just vanish completely. That’s not the result of any calculation one can make. It’s only a determination—say, a physical one. If I believe in the laws of physics with absolute certainty, then I’ll say that this is—what? That they’re eternal. Yes. Then I’ll say that this is zero probability, but the statement that it has zero probability is the result of the assumption that it’s impossible. In the lottery case it worked the other way around. The statistical calculation gave me zero probability, and then I say it’s not likely to happen. It’s possible, but not likely to happen. The zero-probability calculation is the result of a calculation. Here, zero probability is the result of assuming in advance that the thing is impossible. Let me give you an example to sharpen the point. A lot of people who argue against the thesis that the world came into being randomly—many of those proofs are built on the very low probability of such a thing happening. There are even calculations that compute one bound or another on the probability that such a thing could happen—the probability that an organic molecule would form randomly or something like that, even before considering the whole world. I don’t know how one can calculate that, but for them it’s enough to show that it’s impossible for an organic molecule to form in order to say that certainly the whole world cannot be possible. Now how is such a calculation built? Usually it’s built as a product of the probabilities of a series of events leading to the formation of an organic molecule. Let’s say an organic molecule forms out of a state in which there is no organic component, in several possible ways. Each such path is built from all sorts of successive stages. Each stage has some probability of occurring randomly. So the probability that this whole branch occurs is the product of the probabilities of all the links that compose it, right? If you need such-and-such an atom to come and circle around such-and-such a particle, and then exactly such-and-such an atom to come, and exactly this to form here—each of those has some probability. The probability that all this happens is the product of the probabilities of each of the individual events composing the whole chain, right? In the end I arrive at some probability that is very small. Now, once we had some discussion about this—it was even formulated in a book, it’s called Equal Discourse. I don’t even remember what from this got in there and what didn’t, because I didn’t like that chapter. It was at Netivot Olam, the yeshiva where I studied. And there someone wanted to make an argument of this kind—he happened to be a chemist, a professor of chemistry. So I told him this is nonsense. It’s nonsense because this calculation only proves that it’s possible that the world was created by chance. Because you can never calculate the probability that an organic molecule forms by chance. There is no such thing, no such calculation. What you can tell me is the probability that it forms per unit time. Because the probability that it forms in an hour is not the same as the probability that it forms in a billion years or in, I don’t know, a billion billion years, right? Meaning, the quantity you can calculate is never really a probability. It will always be a probability per unit time. So what is the probability that this forms in an hour, in a year, I don’t know exactly, something like that—and you get very, very small numbers. So let’s say you get to one in a billion probability that such a thing forms in a year. That’s just an example—it’s much smaller than that, doesn’t matter, only for illustration. So what does that actually mean? What it means is that if you wait a billion years, then the average number of molecules that form randomly is one. Right? Not that the probability that a molecule forms is one, but that the number of molecules formed randomly over a billion years is one. Meaning that what you’re really claiming is that it’s possible—in other words—that if the world is not newly created, then

[Speaker D] Or not newly created, or

[Rabbi Michael Abraham] newly created but a very, very long time ago.

[Speaker D] Meaning, if the world has existed infinitely many years, then…

[Rabbi Michael Abraham] Meaning that the result of such a calculation never gives a probability; it gives a rate. It gives the probability per unit time that such a thing will come into being, and therefore by definition, whenever you do such a calculation, you are actually assuming that it is possible. You will never manage to prove that it is impossible that way. On the contrary: if you do such a calculation, you are really assuming that it is possible. So if I say that it is not

[Speaker D] possible, maybe all you’re really saying when you say that it’s improbable for a

[Rabbi Michael Abraham] molecule to form,

[Speaker D] you don’t actually know—you’re saying, you’re claiming here that according to the knowledge we have, it can’t be more than

[Rabbi Michael Abraham] ten to the minus two hundred per unit time, per hour…

[Speaker D] Yes, let’s say. Meaning that’s what you’re saying here, right. But then you’re hanging one phenomenon on another; you’re saying if so, that means that…

[Rabbi Michael Abraham] What phenomenon on another? That is the meaning of the result. The meaning of the result is that if you wait long enough, it will happen. Right.

[Speaker D] In other words, you’re also saying how long.

[Rabbi Michael Abraham] Fine. No—the bottom line is that you’ve just calculated the age of the world. You say probability—you can now determine the age of the world. Exactly. Fine. So what have you refuted? All this did was help me calculate the age of the world. You can’t… you can say: this doesn’t fit the current calculations and the age of the world. That yes, if you add that. Right, it can refute. But usually that doesn’t appear there, and that’s one of the problems with these arguments. No, that I agree with. But then, fine.

[Speaker C] Now what is Alvarez’s claim? Have you heard the claim that sixty-five million years ago all life on earth was destroyed? And then indeed the probability—and then to say that sixty-five… this is a claim by someone named Alvarez, a Nobel Prize winner in physics. Alvarez, Alvarez. Have you heard the name?

[Rabbi Michael Abraham] Not the thing itself. Fine.

[Speaker C] So after the ceremony in Stockholm he traveled with his son, who had just received his doctorate in geology, and they went on a trip in Italy. And he said, explain to me what I’m seeing. And his son couldn’t sell his father stories; he said, I’m sorry, this is impossible, and from that various things were born. In any case, there is no living creature that crosses a geological layer older than sixty-five million years. Some ecological disaster happened, for which there are all sorts of

[Rabbi Michael Abraham] explanations, and from that disaster what happened made it possible for things to arise again.

[Speaker C] And sixty-five million years is roughly like the probability that a fly would suddenly form out of the garbage heap in your yard.

[Rabbi Michael Abraham] Yes, no—so that is a claim that definitely is a claim. But the claim that says there is some probability and it is small—first, it’s not a probability but a rate; and second, once you say there is a small rate, then one divided by the rate will tell you how long you have to wait for the thing to happen. So you are actually saying that it can happen. When you say it cannot happen, that claim is never the result of a calculation. When you say it is impossible—not just low probability, impossible—that is never… no statistician will ever be able to do a calculation. Understand how a statistical calculation is built: it is a product of the probabilities of successive events. A product never gives zero unless one of the multiplied factors is itself zero, right? So forget the whole product—if you already know one factor is zero, then you already know everything. You don’t need any statistical calculation. It never gives a result that is zero. Never. Only if it is one divided by an infinite number of possibilities, as we said before. But a process calculation never yields zero unless one of the links in the chain itself has zero probability. But how do you know that? That is not the result of a process calculation. You know it because it is against the laws of physics or biology or whatever it may be. You actually know it not because of a statistical calculation. You know that it is impossible. It is impossible—not that it has zero probability. It is impossible. Something you call impossible is never the result of a calculation. Okay? Now, fine, that was just to close that parenthesis. What the Ohel Yehoshua, Rabbi Diskin, is really saying is that to hit the moment of midnight, or the moment when the Holy One, blessed be He, is angry—if it really is a mathematical instant,

[Speaker B] there’s a difference between those two.

[Rabbi Michael Abraham] Yes, but I’m saying: even if it were a mathematical instant, then it would be impossible—not just zero probability. There is no such moment. Right? It’s impossible; there is no such moment. It is only a transition between states; it is not itself a state. Right? Now here he is mistaken. Why is he mistaken? Because this is actually an event that is possible with zero probability; it is not an impossible event. To hit that moment—since such a transitional moment as, say, the anger of the Holy One, blessed be He—

[Speaker B] Anger is a duration.

[Rabbi Michael Abraham] The anger of the Holy One, blessed be He, is indeed a duration. Now let’s assume that the anger of the Holy One, blessed be He, occupies, say, a discrete instant of time, fine? It is impossible to hit it. Why? Because there are infinitely many such moments throughout the night, and in every minute there are infinitely many such moments, yes? And therefore, one cannot hit that moment. What does “cannot” mean? The probability is zero, not that it cannot happen. According to his formulation, there is no such moment. It’s not that there is nothing to aim at—it’s impossible, not a result… not because there are so many moments and you don’t know which one is the right one. There is no such moment—that’s what he says. And that’s impossible.

[Speaker B] He’s not referring to the anger of the Holy One, blessed be He.

[Rabbi Michael Abraham] Doesn’t matter, it’s midnight, it’s not important. No, no, let’s talk about midnight, I don’t care. It’s defined, but I think

[Speaker B] that midnight is also the same thing.

[Rabbi Michael Abraham] I think midnight is also the same thing. No, anger is a duration. I think midnight is also a time—that’s what I want to say. Midnight too is a time. Only what? It is a time that is a point and not an interval. What does that mean? There are many paradoxes that relate in general both to time and to space, built on this play between a continuum and discrete points. Usually we conceive of the continuous line as a collection of many points standing very densely one next to another. But that is an incoherent conception. Meaning, in mathematics you cannot formulate such a theory of a continuum coherently. And so one arrives at what is called infinitesimal calculus, which relates to a continuous line—let’s say in popular language—as composed of infinitesimals, composed of infinitely small intervals, but intervals. What’s the difference between a point and an infinitesimal? Both have zero length. But a point has dimension zero, while an infinitesimal has dimension one, because it is an interval. It is an interval that is very, very small. What I mean is: the dimension of an area is two dimensions, of a volume three dimensions, a line is one dimension, right? A point is zero dimensions. Right? A point—each thing is qualitatively distinct from the other; it’s not a quantitative question. It’s not that I can take infinitely many points and make a line out of them. I can’t take infinitely many lines and make an area out of them, and not infinitely many areas to make a volume. I need to go up a dimension. I don’t need a lot more of the same thing; I need something of a different type. By the way, there’s an interesting Maggid Mishneh in chapter 17 of the laws of Sabbath. The Maggid Mishneh asks there regarding a side-post: Maimonides says that one may make a side-post from asherah wood. So the Maggid Mishneh asks: but a side-post has a required measure—ten handbreadths.

[Speaker D] We know the rule is that it is considered crushed to nothing

[Rabbi Michael Abraham] its measure. Anything that requires a measure cannot be made from something from which one may not derive benefit, because it is considered crushed to nothing as far as its measure is concerned. So how can it be that one may make a side-post from asherah wood? So the Maggid Mishneh says: yes, it has a measure in length, but it has no measure in width. And about that you cannot say it is considered crushed to nothing as far as its measure is concerned. What does that mean? When you ask yourself how much material is needed for a side-post—the answer is zero. There is length, yes, there is a measure for the length, but there is no minimal quantity of material you need. If there were a measure for width, depth, and height in three dimensions, then there would be some measure of how much minimal material is needed for there to be a side-post. But when the measure is only in one of the three dimensions, then in fact there is no measure for the side-post. You can say it is considered crushed to nothing as far as its measure is concerned—even though it is burned, still zero material is enough for a side-post. It’s the same principle. In other words, we are descending a dimension; it is a different type, not just less of the same thing. And can mathematicians make an eruv? Yes. So apparently, for any body in a certain dimension, if I want to divide it into two, I have to do that by means of a body one dimension lower. When I take a volume and want to split the cube in two, I have to pass a surface through it, right? A surface that cuts the cube. A surface is two dimensions; a cube is three dimensions. If I want to split a surface in two, I have to pass a line through it. A line is one dimension; it divides the two-dimensional thing in two. When I want to split a line in two, I have to place a point. The point is dimension zero; the line is dimension one. Meaning, one always has to go down a dimension. The body that divides…

[Speaker D] What? The meeting point of the lines…

[Rabbi Michael Abraham] The intersection is a point. I don’t need a line for that; a point from within the line is what divides. It’s not the line that divides; a point within the line is what divides that line. Meaning, I don’t need there to be a line there; that’s not what matters to me. So in fact it follows that in order to cut a body of a given dimension in two, you need something one dimension lower. Now when I look at the time axis—and that, after all, is our discussion—the time axis is composed of infinitesimally small intervals, these infinitesimals, because it is like a spatial axis; that is, every continuous axis is composed of infinitesimals. What is an infinitesimal? It is an interval that is very, very short, as short as we wish—meaning tending to zero. It is an interval whose length is zero, but it is not a point; it is an interval whose length is zero. So that means every segment of time will always be an interval, however short, but always an interval; its dimension will be one. Right? What is a time point? A time point is something of a different quality; it is not really time at all, because time is always duration, always some interval, however short, but still an interval. A point on the time axis is not really time, apparently; it is something else, a different kind of entity—if one can even call it an entity. It is something else. So when you divide midnight into two—before midnight and after midnight—the point that divides it is a mathematical point. There is such a point. It is not true that there is no such thing; there is such a thing, but it is a point, not an interval. There is no infinitesimal located at midnight. That is true: there is no interval located there that I can call midnight, of any length whatsoever. But there is a time point. It is not true that it does not exist at all; there is a time point called midnight. When I draw a line, like the line of the night, the time axis of the night, there is a certain point that divides that line in two, and that is called midnight. In that sense it is not essentially different from time. It is a time point and that is a time point. Now, it is a point, so it is true that it is a different quality. You can say that it is not really time in the usual sense. But there is such a thing; it is something that exists. He describes it only as a transition, as though there is no such thing at all. There is such a thing; only its dimension is one lower. Its dimension is zero and not one.

[Speaker B] It’s zero-time, possible.

[Rabbi Michael Abraham] Exactly. Exactly. And now what’s the point? You can’t hit midnight—not because it is impossible in the strong sense, not because it is impossible, but because the probability is zero. Meaning, the probability of finding one point out of a continuum of points—that is one of the lotteries we spoke about before, right? The probability is zero. So when I say that it is impossible, I don’t mean to say that it cannot happen. If I shoot randomly at some point, I will never hit it—not true. It could be that I do hit it; the probability is zero. I will always hit some point. The probability that I hit the right point is zero, because there are infinitely many such points. So when I say that you can’t hit midnight, I do not mean that you are doing something impossible, but rather that you can’t because the probability of success is zero. That’s all; that’s what is meant here. So it turns out that there is a time point, there is a point, there is meaning to a point on the time axis. It is just something of a different quality—it is not an interval, it is a point, its dimension is zero. Okay? So the impossibility of hitting it is really a statistical impossibility, not something absolutely impossible. Now it depends. If you are talking about human beings, about human actions, then you can say it is also impossible in the strong sense. Why? Because any human relation to time is always to an interval; it is never to a time point. I don’t know of any action I can perform that lasts a time point; I don’t think there is such a thing in human action. So one could say that when a person wants to hit that point, it is not even zero probability; it is really impossible. Because a human being cannot even choose a discrete time point. If a human being could choose a discrete time point, the probability that he chooses the right one is zero, but it could be that a human being cannot choose a discrete time point at all—there simply is no such thing. And because of that, it may indeed be impossible in principle. That’s a side remark. Now let’s see a possible implication. There is a passage in the Talmud that discusses whether exact coincidence is possible. What does that mean, whether exact coincidence is possible? We have two things, either in space or in time, doesn’t matter—can they both occur at exactly the same moment in time? Or can two things be exactly the same length? Exactly on the dot, meaning precisely. Can such a thing happen? So the Talmud says no: exact coincidence is impossible. That’s what the Talmud says. So let’s see an example. In the Mishnah in Bekhorot it says as follows: A ewe that had not previously given birth and then gave birth to two males, and their two heads emerged at once. The two heads emerged together. Rabbi Yosei HaGelili says: both belong to the priest, as it is said, “the males are the Lord’s.” “The males” is plural—even two, both belong to the Lord. And the Sages say: exact coincidence is impossible; rather, one belongs to him and one to the priest. What is written in the verse, “the males are the Lord’s”—they may agree with Rabbi Yosei that if there are two firstborns, both would go to the priest, no problem. It’s just that there are never two firstborns. It simply does not happen. Why? Because exact coincidence is impossible. It can never happen at exactly the same moment, with both of them bringing out their heads at exactly the same moment. Never. You cannot align two things to be exactly at the same moment. Rashi says: exact coincidence is impossible, that their two heads emerged as one; rather, one emerged first, but we do not know which one it was. We don’t know which of them came out first. Because of that, later in the Mishnah there is a dispute among the tannaim as to how, nevertheless, one is given to the priest—which one of the two to give him. The smaller one, the…

[Speaker D] Doesn’t matter. It’s like a race, a photo finish where you can’t decide who was

[Rabbi Michael Abraham] first, but with technology too you can never really do such a thing. In a moment we’ll see that. We’ll get to it, because this is exact coincidence by human agency and this is exact coincidence by Heaven’s agency; we’ll get to that in a moment. So here Rashi says it cannot be that both emerged as one. Two things emerge from Rashi; really one principal thing emerges from Rashi. Rashi claims that this thing cannot happen—not just that I cannot know it happened, but that it cannot happen. There is no such thing. The two heads never emerge together, right? That’s what Rashi says. It cannot happen. If, in principle, it could happen but I just don’t know, fine—then I have a doubt. Maybe the two did come out together; who says not? Rashi says there is no such doubt. It cannot happen. No, no—they never come out together.

[Speaker D] Now what does “it can never happen” mean? Because if over there we don’t know, but it is possible, then all it does is put us into a state of doubt. Okay, but Rashi wants to say it is not a state of doubt, but that it is clear that… that the obligation for two firstborns was never created. Right. It’s not that we are in doubt whether an obligation was created. There is no such obligation.

[Rabbi Michael Abraham] Exactly. But on the other hand, when we ask ourselves which of the two kinds of impossibility we defined earlier Rashi means here—no, that’s the problem.

[Speaker B] Here Rashi says it is impossible.

[Speaker D] And not just that he doesn’t know.

[Rabbi Michael Abraham] Everything begins

[Speaker B] from the question whether they came out together or not. And if not—if they did not come out together, if there is no possibility that they came out together—then the question is what is given to the priest. That’s what I said.

[Rabbi Michael Abraham] After all, later in the Mishnah they talk about this. There is a tanna who says: “the burden of proof is on the one who seeks to extract from another,” meaning let him prove that the more valuable one emerged first. Fine, there are solutions to this. But I’m saying: first of all, these views that say it is impossible for both to emerge simultaneously—Rashi says impossible. Not that we don’t know, but impossible. Right? Why is it impossible? What, is it not possible that it happens? Of course it is possible. It’s just zero probability. Right?

[Speaker D] Rashi wants to say no, there are no phenomena… there is a principled philosophical question whether in principle there can be two occurrences in nature that are completely identical.

[Rabbi Michael Abraham] Exactly. That is the question. And the answer is yes.

[Speaker D] Rashi claims no.

[Rabbi Michael Abraham] I think what Rashi is saying is that the probability of it is

[Speaker D] zero. No. Rashi says how…

[Speaker B] it is

[Rabbi Michael Abraham] impossible

[Speaker D] to make exact coincidence, that two heads emerged as one.

[Rabbi Michael Abraham] But that is not true. That is not true. If that’s what Rashi means, then he is saying something incorrect. Because it is obvious that it is possible. Obviously possible. If you say this is a problem in the animal’s physiology—why?

[Speaker D] How would you define what the first emergence is?

[Rabbi Michael Abraham] No, no, it has nothing to do with how I define it. Suppose I define

[Speaker D] that the hair sticking out farthest from the head…

[Rabbi Michael Abraham] Doesn’t matter. It doesn’t matter how you define it. There are two possibilities that need to be distinguished here. Meaning, if you’re talking about a problem in the physiology of the animal, then certainly that’s not what is being discussed—that two heads cannot emerge because of some physiological issue. Because otherwise they wouldn’t connect it to the general topic of “exact coincidence is impossible,” which is a general topic. Here it would be specific to this case.

[Speaker D] Two occurrences always have in principle something…

[Rabbi Michael Abraham] No, no, that claim is not correct. Fine, but that claim is not correct. Because if you say it’s not a physiological problem—right? We agreed on that. Otherwise it wouldn’t be connected to the general topic of “exact coincidence is impossible.” It could be that in the physiology of an animal I would think this way, but regarding the red line in the Temple I would think differently. What connection is there between the two questions if this is a result of physiology? Rather it is obvious that physiology is not the issue. So what is? There are two events taking place, and Rashi says: how can it be that both fall at exactly the same moment? The probability of that is zero. What does that mean? Obviously it is theoretically possible. Suppose one happened at 12 and three seconds and a point, right? All the way down, at some given instant. The second happened sometime in that same region. In each of the moments in that region it could happen with equal probability, including the same moment as the first one. That too could happen. After all, the probability that it was at the same moment is zero. You cannot say it is impossible, because that is simply not true. It is just a random draw of a moment from a continuum of moments. So the probability is zero, but it is possible. On the theoretical level it could have happened. Rather, what Rashi wants to say is that something whose probability is zero should not, for us, be taken into account as a possible side of a doubt. Rashi says it is impossible—he did not mean physically impossible. He means that when you discuss the laws of doubt here, you have to think how many possibilities there are. There is the possibility that A emerged first, there is the possibility that B emerged first, and there is the possibility that both emerged together. Rashi says: since the possibility that both emerged together has zero probability, whereas the probability that A emerged first is 50 percent and the probability that B emerged first is also 50 percent, therefore you cannot present this as a three-way doubt. You cannot say there is a doubt here whether this one emerged first, or that one emerged first, or both emerged together, because these are not equally weighted options.

[Speaker D] This is 50 percent, this is 50 percent, and this is 0 percent. Why would you place a zero-percent

[Rabbi Michael Abraham] option on equal footing with two options of 50 percent? So Rashi says that since the probability is zero, then from a halakhic standpoint it is impossible. Not that it is really impossible, because it is not true that it is really impossible. Halakhically it is impossible. When we make the statement “exact coincidence is impossible,” the meaning is not—even according to Rashi, and I think many later authorities didn’t understand it this way—but it’s not correct. Even according to Rashi, when Rashi says “exact coincidence is impossible,” he does not mean literally impossible, because Tosafot say it is possible, we just don’t know. The problem is with us, not with reality. But Rashi says no, it is a problem in reality itself; it cannot happen. Rashi does not mean it cannot happen. He means that the probability is zero. He just says that because the probability is zero, you cannot take that side as a side about which we are in doubt. You are not in doubt about an event whose probability… perhaps one might say at most that you cannot prove what Rashi meant. Maybe Rashi also meant… it could be that Rashi intended to be mistaken. But the principle of charity in interpretation always says that when you interpret someone, you interpret him in a way that does not make him say something false. And this is such a severe mistake, to say something utterly wrong. What do you mean? It is obvious that it could be that both fall at the same moment; it could happen with zero probability. It’s like drawing—doing a lottery once… a calculation. You have infinitely many possibilities, one of them happened. You do two drawings, fine? And in those two drawings you pull whole numbers out of the set of whole numbers. I ask you: what is the probability that in two successive drawings the number two comes out? Zero, right? But what kind of zero is that? Does that mean impossible? It is possible. So that means it is zero probability but possible. But those are numbers.

[Speaker D] These physical phenomena—what are they if not numbers?

[Rabbi Michael Abraham] He’s asking you at what moment it happened. A moment is a number. Yes, but the phenomenon itself… But a moment is a number. You can’t quantify it, I don’t… what difference does it make? However you quantify it. The moment is a number. Whatever you define as the emergence, define it that way.

[Speaker D] Certainly if I create here two human beings such that they are completely identical.

[Rabbi Michael Abraham] Yes, the probability is zero and it can happen. Absolutely yes. Unequivocally. Why not?

[Speaker B] Hypothetically, theoretically, a uniform distribution—

[Rabbi Michael Abraham] uniform distribution, assuming again—unless there is some issue here, a non-uniform distribution, some correlation between the events. But here there is no correlation between the events. Once there is no correlation between the events, there is nothing.

[Speaker B] From when can something be defined as a doubt?

[Rabbi Michael Abraham] Apparently only something whose probability is non-zero, something that occupies an interval and not a point. Something that occupies only a point—you don’t take it into account as a side in a doubt. That is what Rashi says. And this needs to be understood well, because usually the later authorities learn that the dispute between Rashi and Tosafot is about the question whether this is impossible—this is how Rashi learns, and apparently Maimonides too—or whether it is possible, only that we cannot know that they emerged at once. And we have a problem on our side because we can never know whether they emerged at once; therefore that is the problem, not a problem in reality itself. It seems to me that this is not really a dispute. That’s the point I want to make.

[Speaker B] I think so too.

[Rabbi Michael Abraham] The dispute between Rashi and Tosafot is not really a dispute, because Rashi too says that it can happen. It is certainly possible. Rashi just says that statistically the probability that it will happen is zero. It may be that Tosafot follows his own view, if you remember, because we saw that Tosafot understands that the moment of the Holy One’s anger has duration. Tosafot does not treat a moment as a time point. If you really treat it as having length, then maybe you can indeed say that it is only our problem and that it is possible. And with a point maybe he also says that it is not possible; Tosafot simply doesn’t think there are points on the time axis. And maybe Rashi thinks there are; I don’t know exactly. Fine? In principle, I think there is not really, in light of what we said earlier, any real dispute here between Rashi and Tosafot, and that is exactly the distinction—the distinction between something that takes a moment of time and something that takes a very, very small interval of time. The question is how one relates to events on the time axis. If there is an event on the time axis, like the anger of the Holy One, blessed be He, or midnight, or whatever it may be, that takes a moment of time, then two such events occurring at once can indeed happen, but the probability that they occur simultaneously is zero. Fine? With intervals it can already be different; there the probability might even be some finite probability. Also in Maimonides, look at Maimonides’ wording: A ewe that had not previously given birth and then gave birth to two males—even if their two heads emerged at once, it is impossible that one did not precede the other. Impossible, like Rashi.

[Speaker D] Here he is somehow even more extreme. Why? Here it means that Maimonides says that it is impossible… there is no such phenomenon that they emerged as one.

[Rabbi Michael Abraham] Yes, Maimonides says: exact coincidence is impossible, that they emerged as one.

[Speaker D] According to Maimonides it cannot happen in any way at all.

[Rabbi Michael Abraham] Yes indeed—“impossible” means the probability is zero. That’s all. It seems clear to me.

[Speaker D] Why do you need to say that?

[Rabbi Michael Abraham] Because otherwise it is a mistake; otherwise Rashi and Maimonides said something wrong. Why should I say they made a mistake? This is a basic rule of interpretation. If you can interpret someone in two ways, why say there is a mistake here? It is certainly a mistake, an outright mistake. Later the Talmud makes a distinction between exact coincidence by Heaven’s agency and exact coincidence by human agency. There the Talmud says: The school of Rabbi Yannai said regarding Rabbi Yosei HaGelili: We have heard him say that exact coincidence is possible by Heaven’s agency; all the more so by human agency? And the Rabbis—by Heaven’s agency exact coincidence is impossible; what about by human agency? After all, in the dispute in the Mishnah, according to Rabbi Yosei, exact coincidence is possible, right? That’s what Rabbi Yosei says; therefore both can emerge as one. So the Talmud says: what case is the Mishnah discussing? It is discussing exact coincidence by Heaven’s agency. What does “by Heaven’s agency” mean? A natural event, not something a person did. It happened—God did it, yes? It is something by Heaven’s agency, meaning a natural event. So if Rabbi Yosei says that in a natural event exact coincidence is possible, then in an event a person performs it is certainly possible. But the Rabbis, who disagree with him and say that in an event… and that is also the Jewish law—that in a natural event exact coincidence is impossible, perhaps by human agency exact coincidence is nevertheless possible? Fine? That is what the Talmud asks. So Rashi explains there: exact coincidence is possible by Heaven’s agency—what does that mean? Such as this birth. And even though no one is particular about it. This birth. The birth of the two firstborns in the Mishnah that we saw. And all the more so by human agency. “Even though no one is particular about it” means: even though no person wanted or caused them to emerge together. No one was controlling the process; it simply happened. And I say that even there exact coincidence is possible, although it happened on its own, even though the probability that it happens exactly together is very, very small—really zero. And all the more so by human agency, where one intends to align some measure or some thing—then certainly exact coincidence is possible. And whoever says exact coincidence is possible by Heaven’s agency, then by human agency it is certainly possible. Why? Because if an event that is not controlled at all can occur exactly simultaneously with another event, then in a case where a person tries to make two events happen together, he certainly can succeed. After all, even without trying there is a chance that it happens, so when I do it manually, then certainly there is a chance that it happens. In contrast, the Sages who say that by Heaven’s agency exact coincidence is impossible—they say there is no such thing; the probability is zero. What happens if a person does it? Perhaps nevertheless exact coincidence is possible? That is what the Talmud asks. And in the end we rule that by Heaven’s agency exact coincidence is impossible—that is according to all views. And by human agency there is a dispute. Tosafot says exact coincidence is possible, and Maimonides says that even by human agency exact coincidence is impossible. It could generally be that this follows their respective views. Why does it follow their respective views? Because if we understand “exact coincidence is impossible” to mean that in reality it cannot happen, there is no such possibility—then what does it help me that a human being is trying to align things? So what if a human being is trying to align them? It cannot happen. It simply will never happen. The probability that it happens is zero, right? And because of that, what is the point of distinguishing between exact coincidence by Heaven’s agency and by human agency? The statistical probability is zero. Therefore Maimonides says—and Maimonides is consistent with his view, like Rashi, that it cannot happen—so Maimonides says: if it cannot happen by Heaven’s agency, then it also cannot happen by human agency. Therefore he rules: exact coincidence is impossible by Heaven’s agency and exact coincidence is impossible by human agency. Tosafot, however, apparently understands that the time axis is composed of intervals; there are no points on the time axis. Tosafot always defines intervals: a moment, one fifty-eight-thousandth, however you define it—according to Tosafot every moment always has some specific length. So Tosafot says: by human agency, if you are already trying, one interval can indeed overlap another interval—unlike a point. Then the probability is no longer completely zero, right? The length of the moment will determine the probability. So Tosafot says: by Heaven’s agency we know exact coincidence is impossible because a random event still has a very, very low probability. But if a person is trying to make two events fall at the same time, and time is not a point but an interval, then there is a chance that it happens. It can happen; at least such a possible side of doubt certainly exists, and therefore Tosafot says that by human agency exact coincidence is possible. Fine? What does “by human agency” mean? For example, the red line—you need the red line on the altar; it has to be placed exactly in the middle to distinguish between blood applications that are made above and blood applications that are made below. So the question is whether exact coincidence is possible. How can you know that the red line is exactly at half the altar’s height? And that is problematic, because if it is not in the middle, then one who sprinkles blood below the red line may be giving blood that is supposed to be given below, but actually giving it above. The blood is supposed to be given below the red line, and he gave it below the red line, but really it should have been above—it should have been above the halfway point. Fine? That can create problems.

[Speaker D] Take a safety margin.

[Rabbi Michael Abraham] Fine, but the Talmud says it is a line. You can—the Jewish law is that all the sprinklings are done relative to the red line. Below the red line, you may sprinkle those that are to be given below; above it, those that are to be given above. The Talmud does not say leave a centimeter just to be safe, or leave some gap. So it sounds like exact coincidence is possible; that is what appears. The Talmud says: why is exact coincidence possible? Because it is by human agency. We measure, and we try to place it half and half. It is not like those two firstborns that are born in a natural process; the process is not trying to make them come out together. So the question is: what is the probability that it happens together? Zero—there is no chance. But if a human being is aiming and measuring and so on, then maybe he can indeed hit the mark. Who says not? But if the probability is truly zero and this is a time point, then even by human agency exact coincidence is impossible if this is a discrete point, and therefore that is indeed how Maimonides rules: exact coincidence is impossible. But Tosafot, who sees this as an interval, then it may very well be that Tosafot understands that by human agency exact coincidence is indeed possible, and that is how Tosafot rules—that by human agency exact coincidence is indeed possible. And Rabbi Diskin, who gave there the example of the moment between

[Speaker D] life and death—that is really an example of an event by Heaven’s agency. Yes, right. It is by Heaven’s agency, but it is more than just by Heaven’s agency.

[Rabbi Michael Abraham] It is by Heaven’s agency

[Speaker D] that the Holy One, blessed be He,

[Rabbi Michael Abraham] tries to time it so that it will happen all at once. So that’s certainly better than something done by a human being. It’s not “by Heaven” in the sense used here. Because in the sense used here, “by Heaven” means something with a lower chance of being narrowed down than something done by a person. Since “by Heaven” is a random event, so why should it be? What are the chances that a random event will fall at exactly the same time? Zero. If a person is trying to time it, then maybe he can. But there the Holy One, blessed be He, Himself is trying to time it, so He will certainly succeed.

[Speaker B] And in the end, that is the wrath of the Holy One, blessed be He.

[Rabbi Michael Abraham] So I’m saying that regarding the wrath of the Holy One, blessed be He, it could be exactly the same. If we’ve already reached the conclusion that moments on the time axis have significance, at least according to Rashi and Maimonides, and not according to Tosafot—if moments on the time axis have significance—then it could be that even with the wrath of the Holy One, blessed be He, the impossibility of hitting the exact moment is a mathematical impossibility, because it’s a point in time, not just that I don’t know. If the conception is that it’s a span of time, then what’s the problem? A person can catch a certain span of time; I just don’t know when He is wrathful. How would I know at what moment He is wrathful? That’s only a problem of lack of knowledge. And Balaam knew? Yes, so Balaam did know—what’s the problem? But if it’s something that is just a moment of time, then it’s not a problem of lack of knowledge, it’s a problem of zero probability of hitting it. Meaning, it’s not just because it’s only a moment—it’s a point in time. And it could be that Balaam even managed that, I don’t know. But all Tosafot says is: not even that; he could only begin speaking there, not actually say something there. Fine. But still, it’s something that is a moment in time, and it could really be just like midnight. So there doesn’t need to be any difference between midnight and the wrath of the Holy One, blessed be He. All right, actually there’s one more point I thought maybe to discuss in this context. I’ll say it briefly, because I want one more sentence after that. It came to me in connection with learning the topic / passage of giving a bill of divorce.