Teshuva – Elul 5783 – Lesson 4

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[Rabbi Michael Abraham] T equals pi. What is the time point? Time doesn’t tend toward anything. Why not? Suppose you take a millionth of a second… no, don’t take a millionth of a second, I’m taking a point in time, don’t drag me into a millionth of a second. A point in time, a point. A millionth of a second is infinitely many time points. And on a continuous axis there are also points. Isn’t x equals pi a point? When I really tend there… no, you’re not tending toward anything. At x equals pi, that’s a point; you’re not tending. Do you know the difference between a point and an infinitesimal? An infinitesimal is a segment of dimension one and length zero. A point has dimension zero. It has no length. Its length is not zero; it has no length. And there are mathematicians who wanted to claim that a point also has… there are mathematical models that… but that’s the simple conception. The simple conception is that a point has no length, not that it has length zero. Because length is something that characterizes things of dimension one, and a point’s dimension is zero. Okay, now, the fact that the time axis is continuous, and space too is continuous, that’s true, but there are points of time and of space. There is a point on the x-axis, there is a point on the t-axis. T is time, right? So we can talk about a point in time and a point in space, and therefore I ask: at which point in time is it moving?

Now, there are all kinds of possible ways to try to answer this. I poked around a bit when I wrote the article, and it turned out to me that they haven’t really solved this paradox, in my opinion. Unlike Zeno’s Achilles and the tortoise, which is just a convergent infinite series—but this paradox they haven’t really solved. Usually they solve it somehow—fine, it’s infinitesimal, as you said, with the limit, yes? What infinitesimal—what’s clear? I mean, try to define exactly what, and you’ll see that at most, if you look at it through the spectacles of infinitesimals, then maybe you’ll speak in a language that won’t allow you to present the paradox—but that’s not a solution.

It kind of reminds me of—do you know Principia Mathematica? There’s that work by Russell and Whitehead, a work that apparently nobody ever got through except the authors themselves. It’s three volumes this thick, and it’s just formulas, there’s hardly a word there, only formulas. I once took it on as a challenge; I got about a quarter into the first volume or something like that, and I shattered into pieces. It’s considered a mathematical masterpiece, and in the end it turned out that apparently there’s a fundamental mistake in it; Gödel’s theorem showed that there’s a fundamental mistake in it. But in the introduction—this I did manage to read—there appears there the theory of types, type theory. And what does it say? He tries to solve all the paradoxes of self-reference. Right? The liar paradox. Right? “All Cretans are liars,” whatever, “I am a liar”—that’s self-reference. A paradox that stems from my referring to myself. Okay? Or the barber who shaves all the people who do not shave themselves, the barber of Seville, right? So the question is whether he shaves himself. If he shaves himself, then he belongs to the group of people who are not shaved by him, right? Because he doesn’t shave those who shave themselves, only those who do not shave themselves. And if he doesn’t shave himself, then he belongs to the group that is shaved by him. So yes, no—in short, there is a whole family of such paradoxes whose basis is self-reference, self-reference to oneself.

Okay, now he proposes a solution, Russell and Whitehead. I say “he,” because you know how with physics books by Landau and Lifshitz the legend says there isn’t a single idea there by Lifshitz and not a single word there by Landau. Meaning, all the ideas are Landau’s and Lifshitz was the one who wrote them. I actually met Lifshitz at the Technion; he came to Israel. But there are legends like that also about Russell and Whitehead—I don’t know if it’s true—that the ideas are all Russell’s. In any case, they wrote—let’s say they wrote—in the introduction to the first volume, they proposed a way to solve the problem, the problems of self-reference. They proposed dividing statements in the language into different levels, different types, and the rule is that every statement can refer only to statements that belong to lower types, not to types at its own height, its own level. Now you understand that statements with self-reference cannot appear, because you can’t refer to yourself, because by definition you belong to your own type, right? You can only refer to lower types.

Is such a thing a solution to these paradoxes? In my opinion, obviously not. All you’ve done is create an artificial language in which it is forbidden to formulate the paradox. If you formulate the paradox—it’s illegal, they’ll put you in jail, you spoke incorrectly, not according to the rules. Fine, that’s always Stalin’s technique for solving paradoxes—whoever says them gets his head cut off. That’s not a solution. When you build a language that doesn’t allow a paradox to be formulated, that isn’t solving the paradox; it’s simply ignoring it. You choose not to look at it, or not to present it.

Okay, and in this context too, my feeling is that when people talk about infinitesimals here, what they’re really saying is: I adopt for myself some kind of language in which it is forbidden to formulate Zeno’s sentence, and then I’ve solved the problem. That is not solving the problem. You built a language in which the problem won’t appear. Okay, that’s good for mathematicians, it’s good—we don’t want a language that contains paradoxes—but it can’t really count as a solution to the paradox, because I formulated the paradox in everyday language, it’s perfectly understandable, and there really does seem to be some kind of problem here.

There’s another suggestion I thought about, namely the uncertainty principle in quantum theory. The uncertainty principle basically says that you cannot know the position and velocity of a particle at the same moment simultaneously. Okay? You understand that if so, then there’s no room for the paradox of the flying arrow, because if you know its position then you can’t talk about its velocity, and if you know its velocity, then you can’t talk about its position. So you can’t say that at every single moment you photograph it and it stands in a different place, because if you choose what’s called the position picture—that is, you choose to look at things in terms of their position—then you’ve prevented yourself from talking about their velocities. And vice versa. That is one of the findings of quantum theory.

But once again, I feel that this doesn’t really solve the problem either. It’s like an English-English dictionary. An English-English dictionary takes one word you don’t understand and explains it with ten other words you understand even less. Okay? In other words, you take something I don’t understand and explain it with the uncertainty principle, which itself makes everyone tear out their hair and not understand what anyone wants. So what did we gain? At most, you can say that the same problem that exists in the flying arrow also exists in the uncertainty principle, and if we understand that, maybe we’ll understand this too. Maybe. But that doesn’t solve the problem, okay? Because now I also need to understand the words in the dictionary entry, not just the word it came to explain. And then I really will understand everything, maybe.

So I’ll offer you the following suggestion. Basically, the claim—maybe this is what you meant earlier. Think about how I presented the paradox. I said: I photograph the arrow at a certain moment and I see that it is standing in a certain place. Then I photograph it at another moment; it’s standing in a slightly different place, and so on. And at every moment it is standing in a different place—so the question is, when is it moving? You said: it’s moving all the time. And the claim I want to make here is indeed that it is moving all the time. And Zeno’s formulation is simply wrong in plain Hebrew. Not mathematically, not in any other way—he is simply wrong in Hebrew. The arrow does not stand at every moment in a different place; rather, it is located at every moment in a different place. There is a difference between standing and being located. When you are located somewhere, that does not mean your velocity is zero. It means that is your position. But it is entirely possible that you have some velocity and at every single moment you are located in a different place. You are not standing in the same place because you have velocity. But you are located at every moment in a different place. When are you moving? At that very moment when you are located in that place, you are also moving.

Now, what confuses people? In my view, infinitesimals actually confuse people here. Why? Because in infinitesimal calculus—or in mechanics, because those are the uses of infinitesimals—we are very accustomed to thinking that there is no such thing as a body moving at a point in time. Or having velocity at a point in time. A moving body moves over an interval—if you like, as small as you wish—but you need an interval in order to talk about motion. You cannot talk about motion at a point in time or a point in space. And that is what leads to all the confusion here. And I claim that you can. A body has velocity at a point in time; the body moves at a point in time. What it does not do at a point in time is change place. And we have to be careful not to mix up the term motion with change of place.

My claim is that saying a body is in motion and saying it changes place are not saying the same thing. “It changes place” is a result or consequence of the fact that it is in motion. It is not a translation. It is not the same statement. To say that the body moves and to say that it changes place are not the same statement. “It changes place” is a consequence of the fact that it is in motion. It is not identical with the claim that it is in motion. And there can be situations in which it will be in motion and will not change place. In a moment we’ll talk about that too. But on the conceptual level, that is what I want to claim.

What am I really saying? Think for a moment—when we define in mechanics, first year physics or anything parallel, anyone who studies physics at the beginning of their studies, they talk to him about concepts like velocity. Say I have some body, a body whose position as a function of time—its position as a function of time is, say, like this, okay? This line here. I ask what its velocity is. They tell him: let’s choose two points, drop them onto the axes, and see how much distance it traveled, how much time that took, and the ratio between those two is the velocity. Right?

Now what happens when the graph is not a straight line? Something more complicated. Okay? For that we have infinitesimals. So what do we do in infinitesimal calculus? I say: let’s say I want its velocity here. Okay? So I take two points on both sides, do exactly what I did here, project them down here, project them down there, calculate the velocity. Then I reduce the distance even more, bring them closer, calculate the velocity again. Bring them closer still, calculate the velocity again. The claim is that when I reduce this to zero—if there is some limit, if there isn’t some problematic sharp corner here—if there is an existing limit, that will be the velocity at that point in time.

But how is this usually understood? Usually it is understood—one writes it like this: velocity at a point in time is the derivative of position with respect to time. Never mind, the point is, delta x over delta t as these intervals tend to zero. Tend to zero. Okay? How far you advanced in distance divided by how far you advanced in time, the delta x and delta t, and you take that to zero. Okay? In the limit, when delta x and delta t go to zero, when delta t goes to zero, then we get the velocity at that point in time. But if you ask a physicist, he’ll tell you that this is a fiction. Meaning, “the velocity at a point in time” means: what is its velocity in a small interval around the point. We call it velocity at a point in time, but really we mean what its velocity is in a very, very small interval around the point. Okay, that is what we really mean. In language we say this is velocity at a point in time.

Therefore the claim that this function, that is, V as a function of T, velocity as a function of time, is basically interpreted as: what will its velocity be around each such and such point in time—but it is always over an interval. A small interval around that point in time, or around another point in time. But then, in principle, this function can give a different value for every point in time. Every point in time will get a different value. That is very strange, because if this speaks about a very small interval around the point, then I would expect that around the point it would have the same value, right? Arbitrarily close to the point, it would give exactly the same value. I’m speaking here in plain, nontechnical language—my apologies to anyone sensitive to precision in infinitesimal calculus. But never mind; the principle is what matters, I only want to explain the principle.

I want to claim something else. I want to claim that velocity exists at a point in time. And the definition I gave here, delta x over delta t when delta t goes to zero, is an operational definition, not an essential one. It is a definition of how you calculate velocity; it is not a definition of the concept of velocity. The concept of velocity exists at a point in time, not only over an interval. How do you calculate it? So I go to a small interval around that point, check the distance divided by the time, and take the interval to the limit where its length is zero, and I get the result. But that is the way to calculate velocity. The concept of velocity itself exists at a point, not in a small interval around the point—in a point. And what is its meaning?

After all, it’s obvious that I can’t be in two places at the same point in time, if we’re talking about a point-particle right now, yes? I can’t be in two places at the same point in time. So what does it mean that it has velocity? The claim is that change of place cannot happen at the same point in time. Meaning, to move from place to place in zero time—not time tending to zero, but zero time, at a point in time—cannot happen. By the way, that’s a logical contradiction, not… moving very fast, at a speed beyond the speed of light, that is a physical limitation. Meaning, you can’t move faster than the speed of light. But to be in two spatial points at the same time point is not a physical limitation; it’s a logical contradiction. Meaning, if you are here, you cannot be there. It’s not a problem of transition speed; you are in two places at the same point in time. There is no speed here at all; it is simply being in two places. That is a logical contradiction. It cannot be. Therefore there is no such thing as a change of place at a point in time. But there is such a thing as velocity at a point in time.

How can that be? Because velocity is the potential for change of place. And it is wrong to identify velocity with change of place. When I want to calculate velocity, I look at changes of place, the rate of change of place, and that is how I calculate velocity. But that is a computational definition—how one calculates velocity. The concept of velocity itself is defined also at a point. We observe change of place if we wait for some interval of time, and then if the body has velocity we will see that it also changes place. But change of place of course requires an interval, and change of place will not happen at a point. But velocity can exist at a single point.

I once thought of an example for this, although they don’t really teach it this way, at least not in physics—I need to think whether this really works—but you know the Doppler effect, how they measure the speed of a car? Right? Once radar devices were built this way; maybe today too, I don’t know. So you send an electromagnetic beam toward the car, the beam comes back with a frequency slightly different from the frequency at which it went out. The difference between the frequencies is proportional to the velocity of the car, and you do the calculation and that’s how you find the velocity of the car. Now here, if you think about it, I measure the velocity of the car by touching it at a point. I hit it at a point in time, it returns, and I know the velocity of the car. It’s not like what I described here, where you have to look at an interval, see where it was before, where it is afterward, and divide by the time that took. So that is seemingly a direct measurement of velocity, not through calculation by way of change of place. So maybe that illustrates—though I’m not sure it’s exact, as I said—but it illustrates this concept I’m talking about, of velocity at a point in time and not over an interval. Okay? It looks at velocity as something not calculated through differences in place divided by differences in time, but something that can exist even at a single, discrete point in time.

Now what is this really saying? It says that the velocity of the body does not mean that it changes place; rather, if it has velocity, that is its potential to change place. How does that potential move from potentiality to actuality? If we wait a little time. If now you track the body for a little time—no matter how small a time you wish—you’ll see that it changes place. That is an indication that at every point in time along that interval it had velocity. At a point. Change of place exists over an interval, but velocity exists at a point. And what I’m basically claiming in order to solve Zeno’s problem is that he asked: when is the body moving? The answer is: it is moving at that very point in time at which you measure it when it is standing. Without infinitesimals and without anything. It has velocity at that point in time where it is located in the place at which you are looking, because it is not standing at that point, it is located at that point and it has velocity. Therefore there is no problem. You don’t need to arrive at any infinitesimals or anything; you simply need to distinguish between being located and standing, and that is a simple distinction in Hebrew. Okay? In my opinion, infinitesimals actually confuse matters in the context of Zeno’s paradox and do not help solve it—quite the opposite.

It may be that from this one can perhaps also understand a bit what the meaning of infinitesimal calculus is, maybe from this also understand the uncertainty principle. In the article I proposed an explanation of the uncertainty principle along these lines. I claimed that one can understand—or at least the complementary principle between position and velocity can be understood through this model. Basically, when you look at a body, the way Zeno looked at it and the way we all look at it, we are basically equipped with a camera. Our eyes are a kind of camera. And this camera sees the body each time fixed, as located in another place. The fact that the body moves is an interpolation we perform. We see that it was here, then we see that it’s here, then we see that it’s here, so from our point of view we see it moving. But really—think about it—that’s how movies are made too, right? How are movies made? You photograph static images one after another at a very, very high frequency, and to the eye it looks as though there is motion here, but really it is a collection of static images photographed at a very high frequency, photographed and projected at a very high frequency. We do not see motion; we see position. That is all we see. Motion is an interpolation our brain performs as a result of viewing the sequence of positions. We simply see one image and then another image and then another image, and in our brain some picture is formed of continuous motion. That is the perspective of a camera.

Let’s try to imagine an alien creature, okay? Unknown to us. A creature whose visual sense is based on an ideal camcorder, not an ideal camera. An ideal camera is a camera whose exposure time is zero. A point in time. Its exposure time is a point. Okay? A fictional thing, but I call it an ideal camera, okay? What is an ideal camcorder? An ideal camcorder is a camcorder that captures the velocity of a body at a point, not by seeing that it changed place and making the calculation and the derivative and basically making the interpolation and reaching the conclusion that it is moving. On the contrary, we see the motion itself, we see the velocity at a point in time. Such a creature would not see place. It would see only velocities. It’s a different type of sensing; we can’t really imagine it, a different type. These are simply two quantities that do not speak to one another. So you can—we basically use a camera, take a derivative, and infer that there is velocity. That creature uses an ideal camcorder, and it would do an integral in order to reach the conclusion that there is place—it is the opposite of what we do. Okay? A different creature, never mind, a fictional creature.

The first perspective is the perspective of a camera, which talks about positions, and velocity is calculated by differences between positions because we have no direct access to velocity; we have access to positions. That other creature, the fictional one, has direct access to velocity. It does not know what position is. Position for it is an integral of velocity. It does not see positions; it sees velocities. In quantum theory, by the way—for those who studied it, never mind, I’ll say it—in quantum theory one studies the uncertainty principle; it is presented within a conceptual framework called the momentum picture and the position picture. These are two different pictures through which one can look at the world. In one of them everything depends on positions, everything is a function of positions. In the other, everything is a function of velocities, of momentum—velocity, never mind. Okay? Each of these pictures is orthogonal to the other. Meaning, they do not speak to each other. If you are in the momentum picture, you have no clue about position. If you are in the position picture, you have no clue about momentum.

The interpretation I presented in that article is that an ideal camcorder and an ideal camera are two forms of perception, one of which gives me the position picture and the other the momentum picture. And if one looks at it this way, then the uncertainty principle is a natural consequence of the concepts themselves. In classical physics I could have reached this conclusion—that there is an uncertainty principle. You don’t need quantum theory for this. I wouldn’t have produced h-bar, for those who understand, but I would have known that you can’t simultaneously know position and velocity. It simply cannot be. And the problem is due to the fact that you are trying to approximate a point by an arbitrarily small interval, as though an infinitesimal is basically the point in your world-picture. But no: in the world-picture of the ideal camera, of the ideal camcorder, the point exists there. It is not some limit of an infinitesimal. It speaks about points; the infinitesimal is an integral over points. Okay? So I hope this came out clear even for those unfamiliar with these concepts. At the professional level I don’t care right now; I only want the idea to be understood.

The claim, in the end, is that when a body has velocity, the velocity exists at every point. The consequence of that is the fact that it changes place. The consequence. It is not equivalent, not the same thing; one is the cause and the other is the effect. Velocity is the potential for change of place, and velocity is not change of place—it is not. For example, I’ll give you an example—and again, in plain, nontechnical language; physicists would be very upset that I present it this way. You take a body and throw it at a wall. So it comes at high speed to the wall, but the wall does not let it continue onward. What does that mean? That it basically has a potential for change of place, but that potential does not manage to move from potentiality to actuality. It has velocity, which is a potential for change of place; it does not succeed in changing place in the direction that the potential wants. So it will come out in another way, through heat or other conversions, okay? But that is an indication of the fact that velocity and change of place are not the same thing.

Physicists, if you ask them, will tell you that when the body hits the wall its velocity is zero. It doesn’t hit the wall at a certain velocity and yet stop anyway, because there once again we are talking about an infinitesimal, not a point. But I claim that is not correct. It hits the wall at a certain velocity and the wall does not let it bring that potential into actuality, does not let it change place. So it will emerge in another form. And that is an indication that velocity and change of place are not the same thing. Velocity is the potential to change place, but velocity is not change of place. Okay, that is basically the claim.

Now what do I want to infer from here? I want to claim that very often when we look at some process, what we see in that process is nothing more than a change of states. A process of repentance—let’s look at a process of repentance. I was wicked, and now I’m more righteous, and more righteous still, until maybe I become completely righteous, okay? So from the camera’s perspective, all I see is successive spiritual levels, right? He is at a low spiritual level, then higher, then higher, then higher, until he reaches perhaps the highest spiritual level if he succeeds in completing that process. In this perspective there is no such thing as repentance. Repentance is an interpolation. All there is is movement between spiritual levels. There is no dynamic, no process; there is movement between spiritual levels.

But it is clear to us that such a transition does not just happen on its own; it just happens. We talked about weakness of will: does the Holy One, blessed be He, do repentance for me, or do I do repentance? And this process, this transition between levels, happens because I am in some sort of process. But in the eyes of a camera you cannot see a penitent. You can see a person at such-and-such a spiritual level, at such-and-such a spiritual level, such-and-such and such-and-such or such-and-such. How can you see a penitent? Only if you look at him with an ideal camcorder. And this person is a penitent even at a certain point in this process. He is a penitent. How will you see that he is a penitent? Because if you wait a moment, you will see that in another moment he will be at a higher spiritual level. But that you will see in the next moment. Now this difference affects our perception of these two things. Because you can look at this process as a process that is basically a systematic transition between different spiritual levels—that is from the perspective of the camera. And you can look at this process with an ideal camcorder, and then I don’t see spiritual levels at all—I’m not interested in spiritual levels. What I see is that the person is in a process. He has velocity. At every point in time he is moving, he is in motion.

Okay? When I say that a person’s movement has value, I am basically claiming that in the transition between spiritual levels there is significance also to the very fact of being in transition, not only to being at the higher spiritual level. A person who has velocity—even if, say, he is also under a wall, he won’t be able to move forward, he won’t reach the higher spiritual level—but if he is in a process, he is a penitent. And he won’t reach the higher spiritual level. But he is a penitent. And his being a penitent has value. That value is measured through the very fact that he is a penitent, not through the fact that repentance leads him to become more righteous. There is value to the very fact that he has velocity, not to the fact that he changes positions because of that velocity. Okay?

Even if he’s going backward? Yes, because still, I’m saying, he chooses, he is in a process; there will be a claim against him—why are you going backward? Just as someone who chooses evil as opposed to someone who chooses good. So he chooses, he chooses evil. Okay?

You know, often they say, for example, in management—you know that every three letters are a management method. Pick any three letters from the ABC, every set of three is a management method. It’s one of the known facts. So never mind, but there are many such management methods that say that the dynamism of a company, of a factory, has value in itself. Usually companies are in a dynamism that looks for how they can improve the situation more. Meaning, the current situation is such-and-such, there are certain problems, I can optimize them, so I can make some change that will let me work more efficiently. What happens if I can make a change in such a way that its output will not be more efficient? It will be different, the same overall, but it won’t change things. Say one link—suppose I have a chain of ten links in the production line, I improve link two but at the expense of link eight, okay? So overall I haven’t improved the process. There is a claim that there is something in dynamism that helps a company. The dynamism itself. The dynamism is not a tool for reaching higher efficiency, better achievements; rather, there is something in movement itself, in the very fact of being in motion, that also has value.

Of course in the end, from the factory owner’s point of view, even that value is measured in money. But in the end people will feel better, more refreshed, more open-minded; that too will probably bring him more income. But I’m saying that the change as such is a result. In the end, what matters is that they were in motion, not that the motion led the factory to a better state, but the very fact that they moved—that itself has significance.

Now this cannot be understood if you understand motion only as transition between states. If you understand motion only as transition between states, then there is no significance at all to your being in motion. You are in one state, then afterward in another state, and if they are equivalent, what did you accomplish? Okay? When you speak about the value of your very being in motion, you are basically saying: I recognize the existence of the concept of motion beyond the fact that it moves me from one place to another, namely the very fact that I have velocity.

And I think that is the meaning of “the penitent is preferable to the completely righteous person.” The penitent is not merely moving from this level to a higher level. If that were all, then he would be on the level of those who are already there. But if I say that the very fact of his being in motion is itself an added value, itself a spiritual advantage, then that means that a penitent is by definition preferable to a completely righteous person. You don’t need all the cute explanations of why yes and why no. It is simply because he has a certain wholeness that the completely righteous person does not have. What is that wholeness? That wholeness is the becoming-whole, yes—the fact that he is in motion toward wholeness. To be in motion toward wholeness is itself one of the forms of wholeness.

And for anyone to whom these last concepts sound familiar—right, this is Rabbi Kook in Orot HaKodesh, part 2. Wholeness and becoming-whole. Exactly. He speaks about wholeness and becoming-whole, and he says this:

“The slowness in the order of reality, the limitation in nature, the external laxity of the constriction within spiritual ascents, the temporariness of miracles—all these uphold the foundation of unceasing elevation, which is the inner foundation of reality, whose boundary lies in its boundedness, so that the descent of the revelation of worldly reality down to its lowest depth and its darkest darkness may suffice for an eternal ascent without any doubt. And in every slow period there is a preparation of power for a faster period”—yes, every standing still is an accumulation of energy for the next movement—“until the highest speed, worlds shall lead us, maidens in quickness, as in ‘the maidservant hurried’; running and returning like the appearance of lightning. And never will the phenomenon of elevation cease, and the additions of light, delight, and life go on growing fragrant and becoming ever more filled with higher and more exalted value, until the form of complete perfection and the form of unceasing becoming-perfect, which comes because of the prior deficiency, become equal together. And the becoming-perfect, whose whole basis lies in the fact that you were lacking, itself, in essence, turns into perfection—the very fact that you are becoming-perfect, that you move toward complete perfection. And the memory of past deficiency will suffice to provide a constant push toward ever-increasing becoming-perfect. And the form of unceasing becoming-perfect will rise above complete perfection.”

That is “the penitent is preferable to the completely righteous person.” Unceasing becoming-perfect rises above complete perfection. Why? Because you have the dimension that you also were becoming-perfect, not only that you reached the state of complete perfection. “A woman of valor is the crown of her husband,” and “the righteous sit with their crowns on their heads,” and so on.

Further on there: “The aim of all being, from the side of the hidden will, the hidden infinite will, as it is revealed to us, is a great counsel of elevation and eternal addition. For if there were no reality of smallness and deficiency, there could only be greatness and fullness, but not constant growth and perpetual treading onward and added blessing.” Yes, if reality were perfect, then it could not become perfect, right? It could not become more perfect. “And even though there is no end to the exaltation of full perfection, which because of its infinity has no exaltation from one level to another, still, included within it also is this sublime power of perpetual ascent. And this is considered as though absolute perfection becomes perfected through the becoming-perfect that comes by way of the appearance of smallness that comes into greatness, and this service is a high need.”

What is he basically saying? He says: the Holy One, blessed be He, is perfect. A perfect being cannot become perfected, because it cannot become more perfect, right? If so, that means one of the perfections is lacking in the Holy One, blessed be He: the ability to become perfected, his being in motion—that cannot exist. So there is a problem here. So he says: perfect perfection, the Holy One, blessed be He, becomes perfected through our becoming-perfect. That is, a deficient world was created—us. Why? Because only a deficient world can become perfected, and the creation of the deficient world that keeps becoming perfected completes the Holy One, blessed be He, who is perfect. And because He is perfect, He cannot become perfected; in order for Him also to have that perfection, He basically created us, and our becoming-perfect completes Him. And that is what he calls “this service is a high need.” In the literature of the medieval authorities (Rishonim) and the kabbalists this is called “the secret of service as a high need.” What does that mean? The Holy One, blessed be He, needs us. Without us there is something He could not do; He is not all-powerful. A perfect being has things it cannot do. It cannot become perfected. The very fact that it is perfect makes it limited in that sense—that it cannot become perfected. And for that He needs us.

Therefore, contrary to how we are usually educated—that the Holy One, blessed be He, does not need us, only we need Him—Rabbi Kook says no, that is not true, and this is the secret of service as a high need. Our service is the need of the Holy One, blessed be He; He needs us. Without us He could not have done this.

Look, for example, at the end of the book of Jonah, which we read on Yom Kippur. The end of the book of Jonah—what is the book of Jonah? The book of Jonah basically deals with an argument about what to do with penitents. The Holy One, blessed be He, sends Jonah to Nineveh and says to him: go bring them to repentance. A sinful city and so on; bring them to repentance so that I will not destroy them. Jonah ideologically disagrees; he has an ideological dispute with the Holy One, blessed be He. Right, “they asked Wisdom: what is the punishment of the sinner?” Right? So that is what Jonah says. If they sinned, let them get hit. What do you mean? Why bring them to repentance? And the Holy One, blessed be He, puts him through the fish and… and the Holy One, blessed be He, puts him through the great fish and the ship and all those messes, and in the end he gets to the gourd, right? There by Nineveh, with the gourd. Then the Holy One, blessed be He, brings a fierce east wind all night, the gourd dies, Jonah asks to die, and then the Holy One, blessed be He, says to him: “Are you so greatly grieved over the gourd?” He said: “I am greatly grieved, unto death.” “And you had pity on the gourd, for which you did not labor and did not grow, and I should not have pity on Nineveh the great city?” Right? With much cattle and so on.

What kind of a fortiori argument is that? It is a completely absurd a fortiori argument. Jonah had pity on the gourd? He had pity on himself. A fisherman loves fish, right? So why does he catch them if he loves fish? He loves himself. Did Jonah have pity on the gourd? He did not pity the gourd; he pitied himself. He needed the shade of the gourd. So what kind of a fortiori argument is the Holy One, blessed be He, making to him: “You had pity on the gourd, for which you did not labor and did not grow, and I should not have pity on Nineveh the great city”?

There are two possible answers. One possibility is to free ourselves from our criminal mindset. The fact that Jonah had an interest does not mean he acted out of self-interest. It could be that he needed the shade but also pitied the gourd; he really did pity the gourd. Besides the fact that he also needed it. The fact that he had an interest does not automatically mean he acted because of the interest. Okay? Apropos of Haidt. Very often, especially in political interpretation, we have this tendency: the moment we discover that a politician did something that fits his interest, automatically he is wicked. It could be that he did something that fits his interest, but he also thought it was the right thing to do. That’s also possible. In principle, that can be true, right? We have this kind of criminal mindset that says: the moment we found an interest, we found a villain. But no. It could be that someone had an interest, but that is also what he thinks is right to do. By the way, in politics that is often the case, because in politics why do you have an interest? Because it will strengthen your party. Why will it strengthen your party? Because that is what your party actually thinks is the right thing to do. It is not an accident that it works out that way. That is your ideology. Agree or disagree, it doesn’t matter, argue about it—but you act in that direction because you really think it is right. So it is not necessarily—in politics especially—it almost compels us to reexamine this correlation we always make between interest and wickedness. Fine. And for our purposes, that is one direction. Just a lesson worth adopting.

The second direction is the opposite. Right, the criminal mindset is correct: Jonah acted out of self-interest. The Holy One, blessed be He, also acts out of self-interest. When He has pity on Nineveh, “pity” in the sense of—He needs Nineveh. He does not pity Nineveh. Just as Jonah did not pity the gourd but himself, so too the Holy One, blessed be He, does not pity Nineveh but Himself. Why did He create Nineveh? Apparently He needed it for something, right? Why did He create it? He wants it to exist. So now you tell Him: look, they sinned, destroy them, what do you need them for. You’re telling Me what I need? I created them apparently because I need them. What do you mean, destroy them? I need human beings, I need the world; that’s why I created it. So just as you had pity on the gourd—“pity” in terms of the criminal mindset—apply your criminal mindset to Me too. I have pity on Nineveh because I need it. Exactly like you. Both possibilities exist as explanations of that a fortiori argument.

For our purposes, what Rabbi Kook says here is exactly what is called “Give strength to God.” What does “Give strength to God” mean? It means that what we do gives strength to God. It completes God. Something that He cannot do Himself, He receives from us the power to do. And what is that? So Rabbi Kook offers a beautiful explanation here. He says there is something the Holy One, blessed be He, cannot do: become perfected. And that is what—for that He needs us, because only we can give Him strength, we can give Him that perfection which He Himself cannot possess by virtue of His own nature.

But all this is still not enough. Let’s continue for a moment. “What do we think regarding the matter of the divine purpose in bringing being into existence?” Why was reality created? “We say that absolute perfection is a necessary existence, and there is nothing in it in potential, because everything is actual. But there is a perfection of adding perfection, and that cannot exist in divinity, for absolute infinite perfection leaves no room for addition. And for this purpose—that this addition of perfection too should not be lacking in being—becoming-perfect, the worldly being must come into existence and therefore begin from the lowest possible bottom, that is, from a state of absolute deficiency, in order that it may always keep going and ascending toward absolute elevation. And being was created in such a quality that the step will never cease from ascending, for that is an infinite action. And in order to guarantee the ascent in the essence of being, the whole was created in supreme exaltation, and that exaltation was greater than the measure that limited content could actually contain.”

Complete perfection is infinite, and therefore we will never actually reach it. We will always be in a situation of progressing toward it. And that is what the Holy One, blessed be He, wants. He does not want us to get there; He wants us constantly to strive there, not to get there, because our essential role is not at all to be righteous. The purpose of creation is that there be penitents, not that there be righteous people. Penitents are not something post factum. Penitents are what we were created for. Because the Holy One, blessed be He, cannot repent. He never sinned. He cannot become perfected if He is perfect. And He created the world so that we would sin and repent, if I return to “we will sin and repent.” For that. If there were a completely righteous person, the world would be unnecessary. For completely righteous people, there is no need for the world. Therefore a completely righteous person is a utopian concept; there is no such animal. Because if there were such a thing, it simply would not have been created. It would be unnecessary. Okay? But it is a typological description of a certain type that helps us analyze ourselves. Okay? We strive toward it, and it is a limit—we will never get there. Okay? And why? Because our purpose is always to keep rising and rising and becoming-perfect, because we constantly need to fuel the Holy One, blessed be He—yes, to complete that which in the Holy One, blessed be He, cannot be carried out by His own power.

Yes, repentance was created even before the world was created. Exactly. Because that is the plan for which the world was created. The world was created for repentance. This is not midrash; the argument here is not midrash. This is the plain simple meaning. In other words, the world was created because it is deficient, not despite its being deficient—because it is deficient. Okay? “Truth was cast to the ground,” right? “Truth was cast to the ground” says: forget it, I’m not looking for truth, I’m looking for striving for truth. That’s why the world was created even though Truth objected. Okay?

“Therefore in the appearance of being in actuality, things were corrupted and powers became entangled with one another, and they engage in fierce struggle until the absolute infinite thought of the good will triumph and everything will be rectified,” and so on. “And together with the elevation of giving place to the completion of an unceasing ascent, which is a special delight through which creation completes the honor of its Creator, we understand in absolute divine perfection two values of perfection. One value of perfection, by virtue of whose greatness and completion no addition of elevation applies to it”—the level of absolute perfection. “But if there were no possibility of addition, that itself would be a deficiency, because perfection that keeps on increasing always has an advantage and delight and a certain exaltation that we long for so much, a going ‘from strength to strength.’ Therefore divine perfection cannot be lacking this advantage of the addition of power.” It cannot be that the Holy One, blessed be He, lacks this very fundamental perfection. “And for this there is in divinity the capacity for creation, the unbounded worldly becoming, which rises in all its values. It turns out that the divine self-soul within being, which gives it life, is its constant elevation, which is its divine foundation and calls all beings to become more perfected,” and so on. Okay?

Now let’s think for a moment—there is another important point here that is very easy to miss. The Holy One, blessed be He, is basically saying—and this starts from the fact that it alludes to the Ari. The Ari talks about the fact that creation was created in order to bring the powers of the Holy One, blessed be He, from potentiality to actuality; that too he writes here. Now what does that mean? I also want to bring becoming-perfect from potentiality to actuality, and therefore I created deficient creation.

There is a point here that people miss when they read this in the simple way. When creation becomes perfected, why is that called completing the Holy One, blessed be He? What do you mean? We become perfected—what does that have to do with Him? He created us deficient, we become perfected, all good—but how does that relate to Him? Why does that complete Him? Are we Him? We come back once again to what I discussed in the previous segments: “Bring us back in complete repentance before You”—the question whether there is identity between us and Him, or whether we stand opposite Him, and I said that it is probably something in the middle; otherwise it is hard to understand how we do repentance.

So here too, if we were created deficient and we become perfected, fine, I understand that we become perfected—but how does that complete the Holy One, blessed be He? What has that got to do with Him? The answer—and this is what he says, and it connects to what he also brings in the name of the Ari—is that the potential to become perfected exists in Him too. Actual becoming-perfect cannot be in Him because He is perfect. Remember the body with velocity that hits the wall? It has velocity, it has the potential for change of place, but it hits a wall and the wall does not allow this to move from potentiality to actuality, does not allow place to change, right? Does that mean the body has no velocity? No, it has velocity. It has the potential for change of place. It’s just that something external stops it and does not let it move from potentiality to actuality.

The Holy One, blessed be He, has the potential of becoming-perfect; He has velocity. The fact that He is perfect means that, as it were, a wall stands before Him; He cannot move onward. There is nowhere for Him to move on to. It’s not a wall; there simply is nowhere. Okay? So what is to be done? The potential for becoming-perfect that is within Him must move from potentiality to actuality through us. The potential is in Him. It is not that our becoming-perfect completes Him; our becoming-perfect is the actualization of the potential for becoming-perfect that is in Him. The potential is in Him. It is not that our becoming-perfect completes Him. Our becoming-perfect is the actualization of the potential for becoming-perfect that is in Him.

And again, “Bring us back in complete repentance before You”—what does that mean? That the potential for becoming-perfect is in Him, but we do the repentance. How? I don’t understand—if we do it, then it’s us; if He does it, then what value does it have? Then He’s doing it. Again I return to that same vague point that I already said is vague: something of His potential is actualized in us. There is some connection between Him and us. We are not identical, but neither are we completely separate. There is something—these two models probably do not capture reality fully. And it simply comes back to us from another direction.

And the point is that the becoming-perfect of this thing is its moving from potentiality to actuality. That is the becoming-perfect. The moving of becoming-perfect itself from potentiality to actuality is basically turning velocity into change of place. Now since the Holy One, blessed be He, Himself cannot actualize His own potential by way of change of place, by way of improving, He created other creatures or another world in which it can indeed be realized, move into actuality. As we said about that body which hits the wall and the wall does not let it move forward, then it comes out as heat. It comes out in some other way, and the potential exists there and in some way comes out. If you cannot bring it out in the form of change of place, it will emerge otherwise. So in our case it emerges through us. In the Holy One, blessed be He, it cannot move from potentiality to actuality. That is basically the claim.

And if that is so, then repentance is not only not post factum but a priori. Not only a solution for someone who sinned, but there is something in this mechanism—that we sin because we are deficient and we try to become perfected—which is itself the purpose of creation. It is not an artifact, not a result, not a bug produced by some problem nobody thought about. It is the source. That is what the whole plan is for.

And therefore it is also clear why there needs to be a commandment of repentance according to Maimonides, or the idea of repentance according to Maimonides, and the Meshekh Chokhmah is not correct. The purpose is not to go back and do commandments or to avoid transgressions. The purpose is to move from the state of someone who commits transgressions to the state of someone who does not. The transition itself is what matters. Not committing transgressions and indeed doing commandments—the commandments themselves take care of that, that is what will happen there, we were told what we need to do. But the obligation or value in being in a process of becoming-perfect—for that repentance is responsible. And if repentance had not been written in the Torah, then we would not know that this too has value, and this is where all the value is. This is the whole story.

The point is not at all to be righteous. The purpose of our being wicked is not so that we return to being righteous, but so that we be in motion toward righteousness. The motion is the goal, not righteousness at all. If right now I could somehow have someone hypnotize me so that I would never commit transgressions and would always do commandments and be meticulous about every minor and major one all my life—am I supposed to do that? I think not. Even though apparently that would bring me to an optimal state—what’s bad about that? Because if that were right, then the Holy One, blessed be He, would have created us that way, without free choice, and we’d all be perfect machines. Why would He not just do it Himself? Why create us at all? This whole story—it’s not written anywhere in Jewish law that one may not, but I think we all intuitively feel that it is not right to do that. It is not right to go to a hypnotist who would do that for us.

Why not? What is the problem, really? That is the best repentance possible. Thus “He who knows hidden things will testify concerning him that he will never return to this sin again.” Wonderful—go get hypnosis. No. The whole story is the progress toward the matter. The work and progress toward it—that is the whole story. The purpose is not to end up righteous; for that you could reach it optimally through hypnosis. The righteousness at the end is a model toward which you strive. Not for nothing do we also never actually succeed in reaching it, and we always fall. “He who knows hidden things will testify concerning us that we will never return,” and yet we do return.

A kind of “according to the pain is the reward”? Yes, but “according to the pain is the reward” not in the sense that because you exerted yourself you deserve some extra prize. Rather, the effort is the value. It is the value. Meaning, it is more than we usually understand it as in argumentative terms, just as there are arguments for punishment and arguments for reward. If I also exerted myself, then I deserve more reward. No—the reward is mainly for the effort. Not only for the act, with the effort merely upgrading the reward. The reward is for the effort itself. That is the reward. That is why we are here.

And therefore, the fact that one falls and rises again and so on—there is no need to panic about that. We are human beings; this is how we were created, this is how we were born, and this is what we are. What is needed is to try, to make an effort. And if we fall, then we fall, and we’ll try again. And this effort again and again is not like some military harassment—filling a barrel with a teaspoon, with a teaspoon of water to fill a barrel—which was the kind of military harassment common in our regions. It’s this feeling that you’re doing nothing, it’s Sisyphus, the myth of Sisyphus, where you keep repeating the same thing without getting anywhere. The repetition itself is progress. It doesn’t matter that we are repeating the same thing. It matters—we should try not to—but we should try not to because the trying is what matters, not so that in the end there really won’t be a “not,” but because the trying is our goal.

Maybe I’ll finish with one remark. The Leshem writes in several places—he brings a certain midrash, Midrash Tanchuma, parashat Vayeshev. And there too, repentance and so on. He is in a process; he simply took the reins in hand. “And Joseph was brought down to Egypt.” “This is what Scripture says: ‘Come, behold the works of God, terrible in His dealings with human beings.’ Rabbi Yehoshua ben Korcha said: even the terrible things that You bring upon us, You bring upon us by pretext. Come and see: when the Holy One, blessed be He, created the world, on the first day He created the Angel of Death.” Right from the start, even before Adam sinned and death was decreed upon him, He already created the Angel of Death. How do we know? Rabbi Berekhiah said: because it is said, “and darkness was upon the face of the deep”—this is the Angel of Death, who darkens the faces of creatures. And Adam was created on the sixth day. The Angel of Death was already created on the first day. How can that be? And we thought that death was a decree upon man because of the sin. “And a pretext was hung on him, that he brought death into the world, as it says, ‘for on the day that you eat from it, you shall surely die.’”

“To what is this comparable? To someone who wished to divorce his wife. When he wished to go to his house, he wrote a bill of divorce, entered his house with the purse in his hand and the bill of divorce in his hand. He was seeking a pretext to give it to her. He said to her: pour me a cup to drink. She poured it for him. As soon as she gave him the cup, he said to her: here is your bill of divorce. She said to him: what is my crime? He said to her: leave my house, because you poured me a lukewarm cup. She said to him: you already knew that I was destined to pour you a lukewarm cup, since you wrote the bill of divorce and brought it in your hand. The bill of divorce was already in your pocket, so what are you telling me, that you took it out because I gave you a lukewarm cup?”

“So too Adam said before the Holy One, blessed be He: Master of the Universe, before You created Your world, for two thousand years the Torah was with You as a cherished one, as it is written, ‘Then I was by Him as a nursling, and I was daily His delight’—two thousand years. And it is written in it: ‘This is the Torah: when a man dies in a tent.’ This was written in the Torah two thousand years before the world was created. Had You not prepared death for creatures, would You have written this there? Rather, You came to hang the pretext on me—thus, ‘terrible in His dealings with human beings.’” And similarly you find that the Holy One, blessed be He, said to Moses, and so on.

This is the conduct of “terrible in His dealings.” What does that mean? Basically the whole game is rigged. This sin—You caused me to sin, Adam says to the Holy One, blessed be He. And the proof? Suddenly You tell me that You decreed death upon me, but in the Torah that preceded the world by two thousand years it is already written that man will die. So what are You telling me, that because of me You suddenly brought death into the world?

Usually people understand from here some sort of deterministic view, that basically even our sins are a result of the Holy One, blessed be He, and the Holy One, blessed be He, is responsible for everything that happens here. To me that is absolutely unacceptable; clearly it is not true. I think what is written here is this idea—the idea that the world was created for sin. You committed the sin and death was decreed upon you, that is true, but from the outset the program of the world was to create imperfect human beings, deficient ones, who would sin, and as a result death would be decreed or some sort of spiritual decline would be decreed, in order that it could be repaired and perfected. That was in the plan from the start. It does not mean Adam sinned because the Holy One, blessed be He, caused him to sin. The Holy One, blessed be He, caused him to be deficient. Now by your own powers, now you failed. You failed because you were deficient. Human beings will always fail because they are always deficient. But we still have responsibility because we could also have chosen otherwise.

In broad terms, of course we will sin, because this whole world was created so that we would sin. And this is the conduct of “terrible in His dealings.” The conduct of “terrible in His dealings” means that the Holy One, blessed be He, comes to us with complaints about sins, but in the end we can say to Him: listen, You created us as beings prone to sin. Why is it, by chance, that all people sin? Everyone, it happens to everyone without exception. So don’t tell me that You suddenly come to me with complaints that I was not okay because I sinned. For every single sin there is responsibility, but in practice, clearly, from the perspective of the law of large numbers, there will obviously be sins. Every person will sin. He was created deficient. And why? Because that was the plan from the start: to create a deficient human being so that he could become perfected, and in this sense the concept of repentance preceded the world, because the whole world was created for this work of spiritual progress, for repentance. That is what the world was created for. Okay? So that we would complete the Holy One, blessed be He, bring His potential of becoming-perfect from potentiality to actuality.

All right, so we have some small comfort as Yom Kippur approaches. May all of us be finally inscribed and sealed for good.