Topics in Talmudic Logic, Lecture 18

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[Rabbi Michael Abraham] There really is such a phenomenon—I forgot what it’s called. There’s a phenomenon of people who hear colors. Literally. Different sounds produce different colors for them. Look it up online afterward, there really is such a phenomenon. Why? These are people whose brains are structured differently. It can happen in one of two places: either in the connection between sensation and the brain, right, in the neuron system, the nervous system that transfers information from the senses to the brain, so it transfers information of sound to the visual center; or in the connection between the brain and the soul. Because at the end of the day, when I see color, that’s in the soul, not in the brain. The color is in the soul, right, these are mental processes. The brain may generate them, but in the brain there are electrical currents; there are no colors in the brain. The phenomena that I experience and talk about are phenomena that exist in my soul, not in my brain, right, in my mental part. So the connection between the brain and the mental part—that’s something I don’t know how to test. Because even if it activates the hearing center in the brain, I have no way of knowing whether your hearing center in the brain doesn’t activate sights for you but rather activates sounds for you. When I ask you, of course you’ll say that you hear this or that sound, because you’ve gotten used to calling those sights, “I hear such-and-such a sound,” so that’s how you say it. But that doesn’t help me; I can never penetrate and know what’s really going on there in your subjective dimension. Okay? Fine, thank you. So the anecdote is interesting. At one time I thought there was proof from the Talmud for the idea that the Talmud understands time as something real, not merely a form of human perception. A Talmudic text in tractate Shevuot—and there’s also one in Nedarim; there are two parallel passages here—Shevuot 20a. I’ll read it to you from here: “What kind of prohibition stated in the Torah? ‘It is forbidden to me to eat meat or drink wine like on the day his father died, like on the day so-and-so died, like on the day Gedaliah son of Ahikam was killed, like on the day he saw Jerusalem in its destruction’—it is forbidden.”

But first I need to give a bit of background. In the laws of vows there are two types of mechanisms through which one can create a vow. One can vow directly, and one can create it by analogy. To vow directly means: I forbid this loaf to myself. “This loaf is forbidden to me.” Okay? And then I’m forbidden to eat this loaf of bread. Analogy is when I take something that is forbidden—I’ve already forbidden it by a vow—and I say: the prohibition that applies to this should pass over to this object. It should be like that one. That’s called analogy. I transfer from this to that. So in one case I’m transferring an existing vow—that’s something from something—and in the other it’s something from nothing. Okay? These are two kinds of vowing, two ways to create vow prohibitions. Now what they’re talking about here is analogy. And they tell you that if today you want not to eat meat, then you can forbid the meat to yourself directly, or you can analogize the meat to something else. To what? “Like on the day Gedaliah son of Ahikam was killed.” The Fast of Gedaliah. On the Fast of Gedaliah you’re forbidden to eat. So the relation to this meat will be like the relation to meat on the Fast of Gedaliah. That’s the analogy. I transfer the prohibition from there to here. But how can you make an analogy when there’s no object that is forbidden? What is the forbidden object that serves as the source from which I take the vow and imprint it onto the meat before me? Where is the vow located beforehand? Where am I taking it from? From the meat on the Fast of Gedaliah? But it isn’t the Fast of Gedaliah now—right now it’s… I don’t know, Passover. What does the Fast of Gedaliah have to do with anything? Apparently the idea is that I am making the analogy to the day. “Like on the day Gedaliah son of Ahikam died.” The day is an object that is forbidden, and I’m saying: just as the prohibition rests on that day, I want it to rest on this day too. Meaning that I see the day as a kind of object on which a prohibition rests, and I take the prohibition from that day and transfer it to another day. That sounds like viewing time as something objective, as an existing entity. Because if it were only a subjective matter, you couldn’t define this as analogy. Analogy requires something in the world that is forbidden. What is the thing in the world in which the prohibition is lodged on the Fast of Gedaliah? The objects themselves are not object-based prohibitions; tomorrow morning they’ll be permitted to eat. Only on the Fast of Gedaliah is it forbidden. There are no forbidden objects here; it is the day that is forbidden. Okay, so that’s the first point I wanted to note. And that’s the point that time is—the question is whether time is subjective or objective. Is it our way of looking at reality, or does it exist in reality itself? And with the implication regarding different timelines: are there really different timelines, in which case it’s subjective—each context has a different subjective timeline—or not? Is there one objective timeline, and the different contexts differ from one another not in the timelines but in the events that happen along the timeline? Different kinds of events happen differently along the timeline.

So let’s try to get a bit into this issue of the flow of time. Well, the flow of time is a very problematic business. Conceptually it’s very problematic. When I say, for example, that some object changes its place, what have I said? That at time t equals 0 it was in this place, and at time t equals 1 it’s in that place. So it moved, right? It changed its place along the timeline. As time passed, something else changed—in this case, place. If I talk about improvement, spiritual improvement, or professional skill, whatever, that too is a process that happens along the timeline. I was less good at time t equals 0; at time t equals 1 I’m better—spiritually, professionally, whatever. So a process of change happened along the timeline. I changed the level of my professional skill, I changed my place, I changed my spiritual level—it doesn’t matter what—my mode of action, whatever you want. Change is always defined along the timeline. When I want to say that time flows, what exactly do I mean? That time changes? Changes along what? After all, everything that changes—I said it changes along the timeline. At t equals 0 it had one character, at t equals 1 a different character, so it changed. What does it mean that time changes? Here it is, it flows—meaning it changes. What does it mean that it changes? Flows along what? That at t equals 0 I was at t equals 0 and at t equals 1 I’m at t equals 1? Is that the flow of the timeline? That’s ridiculous. It’s like saying I change place because when I was at x equals 0 I was at x equals 0, and when I’m at x equals 1 then I’m at x equals 1. The flow of place, or change of place, is defined along the timeline, not along the spatial axis. So along what is the change of time, the flow of time, defined? There is no axis along which one can define the notion of the flow of time. Flow along what? To define something as flowing, I need to assume there exists some timeline here, and the thing changes along it. But when I’m talking about change in the timeline itself, then along what does it flow? This has no meaning at all. It is conceptually empty. It’s not a problem that I can’t quite detect it, that it’s elusive, but rather that it isn’t at all clear that the statement “the timeline flows” has any meaning. Flows along what? In what sense does it flow?

But on the other hand, there is still some feeling that there is something dynamic about time. Things happen over time. And our feeling is not the same with regard to space. In space I can stand like this and nothing in space changes, right? But time does change. I stand like this, wait a few seconds, and I arrive at a later time. So somehow the timeline does not behave like a spatial axis. There is a difference between them.

[Speaker D] When you stand in place, then only you are standing in place, while everything else in the world is in motion.

[Rabbi Michael Abraham] No, let’s say the world isn’t moving. Everything stands still.

[Speaker D] If the whole universe is frozen, then there is no time.

[Rabbi Michael Abraham] Why is there no time? Who says? Of course there is time.

[Speaker D] No, if we were talking about motion, then time has no meaning.

[Rabbi Michael Abraham] No, you’re assuming that without motion there is no time. I’m saying the opposite: without time there is no motion. Time comes before motion. There is time, of course—time flows. Even if everything is frozen, what difference does it make whether I’m frozen by myself, you’re frozen by yourself, or both of us are frozen together? If time flows, then it flows. Why should that depend on…? You’re assuming subjective time. You’re assuming a subjective conception of time, and then what you’re really saying is that this is only our way of describing things in motion.

[Speaker D] I can’t understand that. I can understand that if nothing changes, then maybe one can say that time exists, but I don’t understand what it means to say that time flows if nothing changes.

[Rabbi Michael Abraham] What do you mean? You were at t equals 1 and afterward you’re at t equals 2. The fact that you see no change around you—time… what difference does it make?

[Speaker D] So what is the meaning of that?

[Rabbi Michael Abraham] I don’t know—that time passed. Nothing happened. It’s only a physical question: can the world freeze so that nothing changes between t equals 1 and t equals 2? That’s a question in physics. I don’t know whether the laws of physics permit that or not—whether there is some stable state in physics that causes the world to get stuck. Okay? But if so, I see no obstacle to talking about the timeline continuing to flow even though the world doesn’t change. Change without time is hard to talk about, but time—I don’t see why it needs change. In order to notice that time passes, many times we need change, because when a change occurs, I understand that time has passed. But that is only my problem—that is, I don’t know how to notice that time has passed except through the fact that things changed. But that’s merely an epistemic question; it’s only the question of how I know that time has passed. But whether it has passed—it passes even without things changing along it. It seems to me there’s also—

[Speaker D] If I’m not mistaken, there are also changes in physics that don’t take time. For example, when an electron jumps between shells, that doesn’t take time.

[Rabbi Michael Abraham] I think that’s not precise, but let’s leave it—it’s too subtle, and it also depends a bit on philosophy, not only on physics. I don’t think that’s correct.

[Speaker E] There is nothing in the world that isn’t a function of time.

[Rabbi Michael Abraham] No—in physics, physics challenges the ordinary notion of time, but there you have to get into more details, and I’d rather not get into that here. So look, there is indeed a book by Richard Taylor called Metaphysics, a kind of popular introduction to this area in philosophy called metaphysics, and there is a chapter there that he devotes to space and time. He tries to show that all the differences we make between space and time are illusions. There really is no difference between time and space. And let me go back to the example I gave you: if I stand here, time passes even though space does not change. I’m at the same point in space but not at the same point in time. And that’s obvious, because I stand in place and change in time. But what happens if I stand in time and change in space? Then exactly the dual process occurs. For example, how can that happen? If there is a long object, okay? Then it is in several spatial places at the same time. Exactly the way I can be in several different times in the same place if I stand still. Anything that is possible—or let me formulate it differently—there is no proposition that establishes relations between space and time such that if you switch the place of time with space and space with time, the sentence comes out nonsensical. Everything you can say about space you can also say about time, and vice versa.

For example, suppose there is a body that moves, and we say that you can’t move backward in time, right? So Richard Taylor says that’s nonsense; of course you can. Let’s look at what it means to move forward in time. In fact, there’s no such thing as moving forward in time, just as there’s no such thing as moving backward in time. What you can say is that at t equals 1 I was at x equals 1; at t equals 2 I am at x equals 2, right? Now let’s switch the roles of space and time, and I’ll say this: at x equals 1 I was at t equals 1; at x equals 2 I was at t equals 2. Is that a valid sentence? Why not? Exactly the same as the first one; there is no difference. But notice why: because I am describing space in terms of time, or time in terms of space. Never time in terms of time or space in terms of space. And the moment the description is a relation of time to space, you can switch them and everything still looks valid. Everything you can say about time you can say about space, and vice versa. There is no sentence you can say only about time and not about space. When you say time flows but you don’t say space flows, that’s an illusion. Try to translate what it means to say time flows, and you’ll see you won’t be able to translate that sentence into something concrete. The moment you do manage to translate it… “Time flows” means: at x equals 1 I was at t equals 1; at x equals 2 I’m at t equals 2—time flowed along place. Right? Fine. That’s called time flowing. But in that sense place also flows. At t equals 1 I was at x equals 1; at t equals 2 I’ll be at x equals 2. Just as time flows, space also flows. What’s the difference? You’re really talking about changes, not about flow. That’s basically what Richard Taylor says. Or let’s put it this way: we flow along time, not that time flows. But then we also flow through space. Or we stand still in time, or we stand still in space. Whatever you can say about this you can also say about that. There is no sentence you can say about time and not about space.

So therefore, Richard Taylor says, essentially—and many connect this claim with relativity theory—relativity theory basically treats space and time as a system of four axes, a four-dimensional system, three spatial and one temporal, and you can even rotate the coordinate system so that time becomes space and space becomes time, and in fact there is no real difference between space and time. Every event in the world is described as a function of the place and the time in which it occurs. Space and time themselves are not described anywhere. By the way, when people try to describe time and space themselves and to quantize them, for example, they don’t succeed. That is why relativity theory and quantum theory still haven’t managed to connect with each other. And I think part of that is because of this point, because they don’t succeed—they don’t succeed in handling space and time as objects. Space and time are axes along which events occur, but when I want to handle space and time themselves, not use space and time to describe events, that’s where I get stuck. That’s where I get stuck, and therefore there is this philosophical perplexity: are there really such things as space and time, or does all of that exist only within me—is it a subjective matter and not really in the world itself?

It seems to me that if we want to talk about the flow of time in a consistent way, then we need to talk about there being two timelines, not one. Basically, when I say that time flows, I asked: flows along what? After all, everything that changes changes along the timeline. When I say that the timeline itself flows, then what axes describe the movement of the timeline? After all, you need space and time to describe the motion of something. I say where it is and at what time. Now when time flows, then what will I say—where is it and at what time is time? Time is always at its own time. Meaning, t equals 1 is always at t equals 1. So what does it mean that time flows? There is no choice, if we want to preserve this intuition that time flows, except to assume that there are two timelines and not one. There is a basic static timeline, and there is a timeline that our psychology says flows, that flows along the static axis. Because if the static axis were not there underneath, one could not speak of the flow of the timeline, because it would have nothing along which to flow.

Just as an anecdote: there was a certain physicist, now retired, named Larry Horwitz. He taught at Tel Aviv University and afterward also a bit at Bar-Ilan; I too studied with him. And one of my friends did his doctorate with him, and I know that he dealt with the physics of two timelines. He tried to develop all of physics—relativity, quantum, everything, mainly relativity, that was his field—on the assumption that there are two timelines rather than one. And he claimed that this solves a great many problems. So I came to my friend who did his doctorate with him, Nadav Shnerb—today he’s in physics—and I said to him: look, the truth is that there is a strong philosophical basis for this claim that there are two timelines. And then I told him this point, that this feeling of time flowing can’t be explained unless you assume there is another timeline over which or along which the flowing time flows. And he said to me, “Well, good morning, Elijah—that’s the article with which they opened the project.” When they opened the project they wrote an article. He said: that was the motivation for doing it. Their motivation for developing physics on the basis of two timelines was exactly this, because otherwise you can’t understand what flows in time, what is special about time.

Now understand what happens. If indeed we are talking about there being two timelines, then maybe I can speak not only about the flow of time, but I can also speak about going back in time. Because all the problems I described before also imply in exactly the same way that to speak about going back in time is just nonsense. Because what does it mean to go back in time? Suppose today is Wednesday. I want to return to Tuesday. What does it mean to return to Tuesday? Yesterday I was on Tuesday. Is that called going back in time? No, because that was yesterday. So what do I want? Going back in time means that I return to Tuesday, but at a time that is after Wednesday. Right? That’s called going back in time. Because there is no problem with being earlier in time. Yesterday I was on Tuesday, today I’m on Wednesday. That’s not called going back in time. Going back in time means reversing the order. That is, saying: I will be on Tuesday, which is supposedly before Wednesday, but I will be there after Wednesday. After I was on Wednesday, I will go back to being on Tuesday. Right? That’s called going back in time. But that’s nonsense. How can I be on Tuesday after Wednesday? Tuesday, by definition, is the day before Wednesday. So in what sense, when I am on Tuesday, is it after Wednesday? When I am on Tuesday, it is before Wednesday—that’s what yesterday was. What does it mean to go back in time? It’s simply empty of content. Various physicists play around with this process, and the question is whether it is physically possible or not. I claim it isn’t a physical problem at all; it just isn’t conceptually defined. There is no such thing as going back in time. To go back in time means to be at the earlier time after the later time. So in what sense is the time earlier? It is earlier because it is before the later time. So how do you want to be—it’s like saying I want to be in a triangle that doesn’t have three corners, I want to be in a round triangle. There is no such thing. If it’s a triangle, then it isn’t round. If it’s Tuesday, then it is before Wednesday, not after it. What does it mean to go back in time, to Tuesday after I was on Wednesday?

And more than that: suppose you tell me, it means being on Tuesday, but with the experiences I went through on Wednesday present within my consciousness. I already carry the history of Wednesday with me even though I am now on Tuesday. That’s called going back in time. But that, of course, is nonsense. Why? Because then it means I’m not on Tuesday. Because when I was originally on Tuesday, I did not have memories of the history of Wednesday. So now when I go back to Tuesday and I’m there with memories of Wednesday, then I haven’t returned to the same time, I haven’t returned to the same state. So that isn’t called going back in time. To return to the same time means to return to the same reality that existed then. But you can’t return to the same reality that existed then. You can be in that same reality—indeed I was there yesterday. To return there means to return to a place that is not that place, but something else, because by definition I return with things I didn’t have when I was there then. And from this all those paradoxes follow—you know, the one about killing the grandfather: a person goes back seventy years, murders his grandfather before he fathered his father, before he begot his father. Okay, so his father is not born. Now time continues to flow, so he too is not born, because if his father doesn’t exist, then he too cannot exist. So who went back in time to kill the grandfather? After all, after he killed the grandfather he can no longer come into being. So if he can no longer come into being, and we keep moving along the timeline, then in the future I also don’t exist. So if in the future I don’t exist, then who was it that went back in time and murdered the grandfather? It’s a paradoxical loop. Therefore there is a claim that on the conceptual level one cannot go back in time. It’s not a physical limitation; it’s simply just words with no meaning, like speaking about a round triangle.

But there is nevertheless some possibility of speaking about traveling in time if we adopt the proposal I mentioned earlier of two timelines. Because then all the sentences suddenly begin to acquire meaning. Suppose we call the basic timeline tau—we’ll mark it with the Greek letter tau—and the timeline that flows along it we’ll call t. Okay? And now I say this: on tau—when tau equals 0 I was at t equals 0; when tau equals 1 I am at t equals 1. So there, time flowed. Time flowed along the tau axis. And now there is also meaning to the sentence about going back in time. How? When tau equals 0 I was at t equals 1, and when tau equals 1 I returned to t equals 0. In what sense is t equals 0 a return after t equals 1? In terms of tau. Not in terms of t. In terms of tau I am afterward; the time to which I returned really is an earlier time. Without this you can’t define going back in time. So this talk too about going back in time basically assumes—most people are not even aware of it, but usually they assume the existence of two timelines. If there are not two timelines, one cannot talk about going back in time. It is simply an empty expression.

Why am I saying all this? I’ll explain in advance why I’m saying it. I brought those halakhic / of Jewish law concepts of condition and retroactive clarification. Condition and retroactive clarification work backward in time. They change history. Right? A future event will happen tomorrow, and it will change the halakhic and legal status of today. So what is happening here? How can a future event change the legal status of today? I will claim that this is some kind of going back in time. But halakhic and legal going back in time, not physical time travel. And all that is required is to define a model. It’s not a question of whether it is possible, because this isn’t physics; it’s law or Jewish law, it’s ideas, not a physical process. What I do want, however, is to propose a model that defines this on the conceptual level. Because if it doesn’t exist on the conceptual level, then even in the legal context one cannot speak about it, not only in the physical context. If it’s only a physical problem—that one can’t go back in time physically—but conceptually it’s defined, then I can say that in Jewish law and in law one can go back in time. That’s how we define our legal and halakhic system. But if the concepts themselves are not defined—the concepts of going back in time—then you can’t talk about it even on the legal plane. Because then it is simply undefined, mere empty chatter. Okay? That’s why it is very important to define the concepts independently of these fantasies about whether there is time travel in physics. One needs to define the concepts for legal purposes.

So let’s keep moving. Rabbi Shem Tov Gefen was a very interesting Jew. Rabbi Shem Tov Gefen was one of the forefathers of Yonatan Gefen, Aviv Gefen, and so on, Moshe Dayan, that whole family. Uzi Dayan. Beginning of the twentieth century. His son was already an older man living in Tel Aviv, died in Tel Aviv, was some sort of poet, I think, or something. I think. In any case, he wrote a book, or articles that were collected into a book, three articles. The book is called Dimensions, Prophecy, and Geology. He had that Hebrew of the early twentieth century. “Geology” there is in an old-fashioned Hebrew form. And the middle article there in the book, by the way, is an article that was published in a mathematical journal in Russian dealing with the nature of prophecy. Very interesting, really a polymath. It came out from Mossad Harav Kook, Dimensions, Prophecy, and Geology. Once I found it in some forgotten archive somewhere, and later it also came out in newer editions. I think you can still find it here and there.

In any case, Rabbi Shem Tov Gefen argued that in religious thought we often struggle with questions of the age of the world. How old is the world? Our tradition says 5,780 years. Okay? Science says about fourteen billion years. So who is right? So Rabbi Shem Tov Gefen says: look, if we adopt Immanuel Kant’s conception, that space and time are only forms of our perception, they do not exist in the world itself, then this problem doesn’t arise at all. Why? Because before there was a human being, there was also no time. Time is merely the subjective form of human perception. So there is no point in asking how long the world existed before the human being was created. From the moment the human being was created, time began. Or this human being who thinks in terms of space and time—depending on where in evolution you place him, whether Homo sapiens from its beginning—5,780 years. Then the concepts of space and time were created. And therefore, in fact, time was born then. Because all of time exists only in human consciousness or awareness; it does not exist in the world itself. So there is no question of the age of the world. That’s what he argued.

Where is he mistaken? According to his logic, then one could also deny the question of when my father was born. Because when my father was born, I was not in the world, and my timeline, of course, also did not exist in the world if I did not exist in the world. So when I ask “when,” the meaning is: along my timeline my father was born. But my timeline did not yet exist then. So that question is illegitimate. That’s nonsense. Why is it nonsense? Because it is clear that even if the timeline is a form of my perception, I still have no problem applying it also to the distant past. Now that I already use this form of perception, I look at the world and I also look at the past, at the world in the past. And now I can ask myself when my father was born. I say a hundred years ago, okay? Just for the sake of discussion. He was born a hundred years ago. I did not exist then, but from my viewpoint today, when I look backward, I say he was born a hundred years ago. There is no problem at all with that statement, as long as I remember that the concepts “a hundred years” are contemporary concepts. That’s how I choose to describe events in the world. Remember—we are talking about Immanuel Kant, that time is a subjective matter, only our form of description of the world. So after all, even in the present world there is no time. When I say that something happens after something else, that is only my expression to describe the relation between events. In the world itself there is no time. So what difference is there between describing the present and describing the past? My view of the past too is made in terms of my subjective timeline, and I can ask when my father was born, and by the same token I can also ask when the world was created—5,780 years ago or fourteen billion years ago. There is no problem with that. It has nothing to do with the question of objective time or subjective time. Subjective time too is simply how to look at what happens in the world. But before I was born my timeline did not exist; after I was born, the timeline was born together with me—it’s a kind of pair of glasses—and now with those glasses I can also look at what happened earlier. It is simply a way of looking at what happened earlier. Fine—so what? I describe things in terms of fourteen billion years, 5,780 years. These are only my forms of description, but they are forms of description of something that did exist in the world itself. Not time—time is only the way I describe it. And that’s all. And that’s what the discussion is about. So is it fourteen billion or 5,700 years? That is a question; it has to be discussed. It has nothing to do with Kant. I think he is mistaken about that.

But now look at what happens in this situation. When I—let’s look for a moment at a condition. Let’s jump for a second to the end, because after all my ultimate goal is to propose a model for how conditions work, how retroactive clarification works. Let’s look for a moment at a condition. So I give you a gift on condition that in two days it rains. A gift from now. If in two days it rains, the gift is yours from now, and if not, then not. So one could understand that, in fact, if it rains in the future, then the gift is yours from now. The fact that I don’t know it, because I don’t know whether it will rain, means I have to wait two days and see whether it rained or not. But that’s only because I don’t know; the gift is already yours from now, I just don’t know it. Okay. And one could say: no, the gift was not acquired, and when the future event occurred it changed the legal status of the gift in the past. There can be causality from the future to the past on the legal plane, even if not on the physical plane. That is not the same statement as before. What is the difference? In the second statement, when I ask whether the gift is now acquired or not acquired, then someone has to answer me: depends from what point of view. From my point of view today, the answer is no or I don’t know. From my point of view two days from now, the answer is that the gift today is acquired. So that means that when I ask about the status of the gift today, there can be several answers, and all of them are correct for the same question. The first interpretation I gave was that there is only one answer. The first interpretation I gave was that at every moment of time there is only one correct answer to the question, but I don’t always know it. The second interpretation says no. From my current point of view, the gift is not acquired. We’ll wait another two days, and from the point of view of two days from now, the gift is already now acquired. Meaning, the status of the gift at this time depends on the time from which I apply the viewpoint. You see that in fact there are two timelines here. The timeline of the observer—from which point in time is he observing—and the timeline, the point in time, that is being observed. And the value of the function—whether the gift is acquired or not acquired—depends on these two timelines. Both the timeline of the gift itself and the timeline of the observer. This is a demonstration of the meaning of describing reality on the basis of two timelines. Okay?

Basically what I want to claim is—maybe I’ll share something for a moment. I’m just sharing with you a file, an empty Word file, and I’ll write a few things on it to clarify. Look. The legal status—let’s denote it by M—is a function of t and T, let’s denote the second one by capital T. Okay? Meaning, if I want to know whether the gift is acquired or not acquired, it is not enough for you to give me the value of t, meaning on which day we stand. You also have to give me the value of capital T, meaning from what point of view you are looking at the question. From the point of view of two days from now, or from the point of view of now. And then, basically, the claim is that the status of the gift is a status defined on the basis of two timelines. And in order to say whether the gift is acquired or not acquired, you have to give me those two data points, and then I can answer you. In the case of the condition, for example, I can tell you that the gift is acquired by you beginning from t equals 0, as long as capital T is greater than 2. If capital T is between 0 and 2, then the gift is not acquired by you at any stage, for any small t. Understand? It’s a function of two variables. In order to get the value of the function, you have to give me two inputs, not only one. But the novelty is that both inputs are temporal. You have to give me two times in order to give me the result of the function. And therefore, basically, Rabbi Shem Tov Gefen, when he asks—when I ask when the world was created, then I say it was created at t equals minus fourteen billion, assuming I’m looking at it with capital T equal to 0 and higher. From the time I was born, from when I have a timeline. But once I have a timeline, I can also look backward on ordinary time, the time from which I observe. I can look at ordinary time and speak also about times much earlier than my own time.

And now the claim is that if I want to talk about going back in time or the flow of time, then look, now I’ll share something else with you. All right, forgive me for this, I’m not checking now how to draw a straight line. Here there is—let’s say, look at this as a coordinate system, okay? Now I describe: the vertical axis is the t axis, and the horizontal axis is the capital T axis.

[Speaker D] Can you see it now? Yes, now you can see it.

[Rabbi Michael Abraham] So look at these two axes. This one, the horizontal axis, is the capital T axis, and this one is the small t axis. And now when I say that time flows, the meaning is—let me take another color—it basically means that as capital T flows, small t flows along with it. I can now define change in small t along capital T. What does going back in time mean? This. A sawtooth. What does that mean? In this segment, when capital T equals exactly this value, what happened was that this time stopped flowing, went backward, received a lower value—I went back two days—and then continued to flow again together with that axis. That is what is called going back in time. All the concepts I can speak about—concepts of going back in time, concepts of the flow of time—can now be defined clearly if I speak about two timelines. Because now I can also talk about a function that is a function of time, a function of two timelines. For example, whether the gift is acquired or not acquired: in order to answer that, tell me at what time you are speaking and from what point of view you are looking, and then I’ll know the value of the function. But when I talk about the flow of time itself, then I am talking about a different function. I’m talking about this function. The function t as a function of T. What did it do to me here? Small t as a function of T. That’s the sawtooth I described earlier. Capital T advances—that is the fixed time, so to speak—and small t advances with it too. Right, on Sunday I am on Sunday. On Monday I am on Monday. On Tuesday I am on Tuesday. A forty-five-degree angle between the two axes. And on Wednesday I go back in time. What does that mean? On Wednesday I go back down one day and then continue moving forward again, continue progressing together with that axis. That is called going back in time. The moment I have two timelines, one of them can flow along the other, can go backward along the other, and suddenly everything becomes well-defined.

And again, I am not proposing here proposals in physics. I am not claiming that this is possible in physics, or that it is defined in physics, or that it is not. I don’t know. What I am trying to do is define a model that gives meaning to the concepts. I can now speak consistently about going back in time, about the flow of time, and then on the legal plane, which does not necessarily depend on physics, I am well-defined when I speak about going back in time. Okay? That is basically what I am trying to gain here.

Now I want to talk a little about the relation between time and causality. Or let’s first define the concept of causality a bit, and then we’ll talk about the relation between it and time. The concept of causality is also a rather elusive concept—that event A is the cause of event B. What does that mean? Usually we distinguish between three components that make up the concept of causality. One component is the temporal component: the cause must appear before the effect. That is the point that interests us, the connection between causality and time. The second component is the logical component: if the cause occurs, then the effect occurs. The cause is a condition for the effect. And the third component is the physical component: the cause produces the effect or brings about the effect. It’s important to me to clarify the difference between the second and the third. The second only says, on the logical plane, that if the cause—say the cause is A and the effect is B—if the cause, then the effect, right? If A then B. For example, I can say that if the sun rose in the morning, then I go to work. Is the sunrise the cause of my going to work? No.

[Speaker E] That’s not logical.

[Rabbi Michael Abraham] No, it is logical. It’s only logical. It’s not a cause. Why? Because the sunrise just is. Exactly. But, but, but it is true on the logical level that it’s a condition. Meaning, if after the sun rises I go to work, or whenever the sun rises I go to work, then there is a temporal connection between sunrise and going to work; there is also a logical connection, but there is no full causal connection, because there is no relation of causation between the two events. So in order for this thing to be, in order for the relation to be defined as a causal relation, there also has to be causation.

Maybe I’ll give you another example. There is an American Jewish logician named Raymond Smullyan, and he argued—there’s the question of astrology—that the state of the stars somehow predicts, or corresponds to, what happens here on earth. Meaning, if you know the state of the stars, you can tell a person what will happen to him, what won’t happen to him, I don’t know, all kinds of things like that. That’s the claim of astrology. In my view this is nonsense—again, don’t take this as any kind of support for that; I absolutely do not believe in it—but I’m speaking here on the conceptual level just in order to illustrate.

Now he says, he brings up that one of the major objections to astrology is an objection from physics, from relativity theory. Why? Because it says that the state of the stars determines what happens in the world at that same moment. But the stars are so far away that this cannot be, because information cannot travel faster than the speed of light. So if the state of the stars right now is some particular state, then it cannot be that this determines events that happen down here at the same time. There has to be some time from the stage at which it happened in the stars until that influence reaches down here. And therefore there is a claim that astrology cannot be correct from the standpoint of physics. That claim is not correct. Besides the fact that astrology is not correct, that claim also is not correct. It is not correct because I think they are not talking about the state of the stars now; they are talking about what I see in the stars now. What I see in the stars now is their state from I don’t know how many years ago—the amount of time it takes for light to get here—and now I see that state. So if that’s the case, there is no obstacle at all to its also affecting the state down here.

But let’s assume for a moment that this claim is a good one for the sake of discussion. So Smullyan argues that he has an explanation that can resolve this. What is it? It could be that the state of the stars really does not cause what happens down here, but rather is in correlation with what happens down here. For example, it could be that there is something that synchronizes what happens in the stars with what happens down here, and it is always parallel. Not because the stars cause what happens below, or because what happens below causes what happens in the stars, but because there is some third thing that synchronizes them both. Still, if I look at the stars I will be able to know what is happening down here, even though the stars are not the reason for what happens down here. But they are a condition for what happens down here. There is correlation, but there is no causal relation. Okay? For example, take two clocks that always show the same time. Does that mean that one of them is the cause of the other?

[Speaker B] No, there is correlation between the two, because someone synchronized them.

[Rabbi Michael Abraham] Right, there is correlation between the two because the clockmaker synchronized them, right? So the fact that there is synchronization between them, and I can say that if clock A shows three o’clock then clock B also shows three o’clock—then that is a logical conditioning. But that still does not mean that there is a relation of causation between them. Therefore, in addition to the logical conditioning, you also need the causal connection in order to define a concept of causality.

I want to deal a little more with—maybe I’ll give an example. I’ll give an example from a halakhic topic: its beginning was in negligence and its end was in an unavoidable accident. In the topic there—I spoke about this not long ago in one of the Zoom classes, I don’t even remember where—in that topic they distinguish between three situations. I’ll do this briefly just in order to illustrate the principle. They distinguish between three situations.

The first situation is when, say, a watchman received an animal to guard, and he opened the door and the animal was stolen. This is called negligence. Okay? It is not called theft; it is called negligence. Why? Because the watchman’s duty is to close the door so that the animal will not be stolen, will not be lost, and so on. So opening the door was the reason the thieves succeeded in stealing the animal. A cause in the legal sense, of course, because the thieves could also have chosen not to steal. Even if the door is open, they have the right to decide not to steal. It’s not that the moment the door is open, the animal is necessarily stolen. But on the legal level they see you as responsible. Meaning, opening the door is considered legally to be the cause of the theft. So you were negligent.

There is a second situation called: its beginning was in negligence and its end was in an unavoidable accident. I received money to guard and I hid it in a shack in the forest. Now that hiding place is excellent protection against thieves. Because no thief would imagine that in an abandoned shack in the forest there are coins. He would not look for that there. He would go to some inhabited house to steal money. So this is considered good protection against thieves. But not against fire. A fire could break out there and burn the money. So I was negligent with respect to fire, but I guarded it well against theft. What happened in the end? Thieves came. Not likely, but they came. Thieves got there and stole the coins. This is called a case whose beginning was in negligence and whose end was in an unavoidable accident. There is a dispute whether one is liable or exempt. In Jewish law the ruling is that one is liable.

A third situation: I opened—you know what? I’ll describe all the situations with the coins; forget the cow. The first situation: I put the coins in the forest and they burned. That is negligence, right? That is exactly what was expected. The forest is prone to fire. The second situation: I put the coins in the forest and they were stolen. Against theft I guarded them well; only against fire was I negligent. And what happened in the end was that they were stolen. So ostensibly what happened was an unavoidable accident; against that I guarded them properly. But its beginning was in negligence, because you did not know that no fire would come. So in principle you were negligent; you were not allowed to put it there. This is a case whose beginning was in negligence and whose end was in an unavoidable accident; about it there is a dispute, and in Jewish law the ruling is that one is liable. Third situation: I put the coins in the forest, and in the end it turns out that the strength of their material was not so great—they crumbled.

[Speaker D] That could also happen at home.

[Rabbi Michael Abraham] Right, that could also have happened at home. In such a situation, according to all opinions I am exempt, except for the Rif in Abaye’s view, which is not the practical ruling. But the Rif, in Abaye’s view in Bava Metzia 36, argues that even in such a situation, where there is no connection between the negligence and the accident, one is liable. But in practical Jewish law it is obvious that one is exempt, according to all the medieval authorities (Rishonim), all the Amoraim, all the opinions except for the Rif in Abaye’s view.

What is the difference between these three situations? I argue that the difference between these three situations is exactly the three components of causality. A case of negligence is a case where you put the coins in the forest and they burned. Now, when you put them in the forest, why was it forbidden for you to put them there? Because there was concern that they would burn. And that is exactly what happened. So on the legal level they see you—you who put it in the forest—as the causal agent of the fact that the coins burned. And therefore you are liable. That is called negligence.

When I put the coins in the forest and in the end they were stolen, then you cannot say that what I did caused the theft; what I did was good protection against theft. What you can say is that if I had not put the coins there, they would not have been stolen, right? Agreed? You cannot say that because I put them there they were stolen, because putting them there is not something prone to theft; it was not expected that there would be theft. But it is true that if I had not put them there, they would not have been stolen. If they had not been there, why?

[Speaker B] They could have been stolen at home.

[Rabbi Michael Abraham] No, because the thieves came there. At home I guard them properly. I’m talking about the thieves who came there. The thieves who came there would not have stolen them. Otherwise that’s a new story. What happened there would not have happened. Meaning, if I had not put them there, it would not have happened. That is a logical condition. There is no causation. My putting them there did not cause the theft, because it is protected against theft when it is lying there. But the logical conditioning does exist: if I had not put them there, they would not have been stolen. So here the temporal and logical relation exists, but not the causal one. First I put them there and afterward they were stolen, so the cause preceded the effect, and the cause is also a condition for the effect. But the cause is not a physical factor producing the effect.

What is the third situation? I put the coins in the forest and they crumbled. In this situation there is not even a logical condition. It would have happened at home too.

[Speaker D] Time—it’s a matter of time.

[Rabbi Michael Abraham] Only time. Meaning, only that first I put them in the forest and afterward they crumbled—only that component of causality exists there. Meaning, the third case includes only the time component. The second case includes the time component and the logical component. The first case, which is ideal, complete negligence, includes all three components: the legal causation in this case, and also time, and also the logical conditioning. Okay. And that is basically the difference between these three things.

By the way, as an aside, why according to the Rif in Abaye’s view is one liable if I did not cause it in any sense? The explanation—Rabbi Akiva Eiger explains this—is that the moment I put it in the forest, I was negligent. The moment I was negligent, I am already liable, because I was not allowed to put it in the forest. What happened afterward is no longer interesting. Why? If the coins had survived, I would still be liable to pay for them; I would just take the coins themselves and return them as the payment. But I am liable in any case. The moment I put them in the forest I am liable to pay, because I was negligent. Now, when the coins did not survive, I do not care why. I am liable to pay and I have nothing with which to pay. I do not have the coins to return—they crumbled. So I pay with something else. That is the claim. That is the claim that if there is no connection between the negligence and the accident, why am I liable according to the Rif in Abaye’s view? Because I am liable for the negligence itself. There does not need to be a connection between the negligence and the accident. The negligence itself obligates me. It’s just that usually I simply return the deposit itself, and that will be the payment I am obligated to pay—what difference does it make. But if the deposit was lost, even through the greatest unavoidable accident, that simply makes no difference. I have nothing to pay, so I have to pay from my own money. Okay, but that is only to explain why it is not something completely absurd.

In any case, for our purposes, I’ll finish here. I’ll just say that what we have seen until now is that causality is made up of three components: the temporal component, the logical component, and the physical component—causation. Okay? That is what is defined as a causal relation. Next time we’ll continue from here. If anyone wants to comment or ask, then you can. More power to you. Okay, so goodbye.

[Speaker D] Yes, Rabbi, I have a small question related to the description of two time axes. Just generally, you said there were some people who wrote an article about it.

[Rabbi Michael Abraham] Wait, one second before you leave, friends, just a second. Before you leave, let me just—yes, okay. Now you can. I just wanted to take attendance; as usual I forget it.

[Speaker D] Yes. So if, say, the graph you drew—if you look at it as a regular graph, say of place versus time—then you could sort of describe its derivative as velocity. So is there some meaning to that with two time axes, some intuitive idea one can think about?

[Rabbi Michael Abraham] The derivative of t with respect to big T, you mean?

[Speaker D] Yes, whether there is some intuition for that.

[Rabbi Michael Abraham] It’s not velocity; it’s the rate at which time progresses. For example, in psychology. A day passes, but it feels like eternity to me because I’m waiting for something. So that means the rate of progress of psychological time relative to physical time is very slow. So the derivative is small.

[Speaker D] So for each of the seven time axes that you said exist, there is a different slope that describes… exactly.

[Rabbi Michael Abraham] Or a slope, or even a more complicated graph, maybe a sawtooth if there is time travel. Meaning, different forms of dependence of t on big T. All right?

[Speaker D] Okay, thanks, thank you very much, a fascinating lecture.

[Rabbi Michael Abraham] Okay, goodbye.

[Speaker D] Bye-bye.

[Rabbi Michael Abraham] Bye. Peace be upon you. We are on the eve of Hanukkah, and we want to reflect a little on the essence of these days. It is written in the holy books: a little bit of light pushes away a lot of darkness. This is a great principle in the service of God. A person should not be alarmed by the great darkness in the world, or by the darkness he has inside his heart. Because a small point of light is enough, one good desire is enough, one commandment is enough, to drive away all the darkness. Why is that so? Because darkness has no substance. The moment you light the light, the darkness disappears. Let us see what the Sefat Emet says about our Torah portion, Vayishlach, and how it connects to Hanukkah. Our forefather Jacob wrestles with the ministering angel of Esau. It is written: “And Jacob was left alone, and a man wrestled with him until the break of dawn.” The struggle is within the night, within the darkness. And who wins? Jacob, when he reaches dawn, when the light rises. And this is the secret of Hanukkah—the light that defeats the long night of exile. King Solomon says in Proverbs, “For a commandment is a lamp, and Torah is light.” What is the difference between a lamp and light? A lamp is a vessel; a lamp is something that holds the light. The light is something spiritual and abstract. So too with the commandment and the Torah. The commandment is the physical act, the vessel, and the Torah is the light that shines within the commandment. On Hanukkah we light lamps; we take the physical act and put great light into it. And this is what we say: a little bit of light pushes away a lot of darkness. The Holy One, blessed be He, helps us, and we need to know that there is a power of light within each and every one. And this is: a little bit of light pushes away a lot of darkness.