Means and Ends – Lesson 2
This transcript was produced automatically by means of artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
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Table of Contents
- Zeno’s arrow paradox: being at a place versus standing still
- Velocity at a point: calculating through intervals versus definition
- Velocity as potential and change of location as indication
- Measurements and velocity: Doppler, relativity, and force
- The uncertainty principle and dual pictures in quantum theory
- Film, vision, and a static perception of dynamics
- Velocity without change of location: collision with a wall
- Repentance, perfection-through-becoming, and Rabbi Kook: the value of potential
- Additional sources for a higher need: Jonah, Hoshana Rabbah, Berakhot, and the Lubavitcher Rebbe
- Dynamics in organizations: the value of movement itself
- Einstein versus Bergson: static time versus duration
- Two time axes and time travel: static and dynamic
- Means and ends: the value of action beyond the result
- Giving a bill of divorce and defining an action: “and he placed it in her hand” versus edge cases
Summary
Overview
The text proposes a conceptual solution to Zeno’s arrow paradox and argues that the failure comes from conflating “being in a place” with “standing in a place,” and velocity itself with actual change of location. It maintains that velocity is defined even at a point in time, even though the operational way of calculating it goes through intervals and differences, and from there develops a general view according to which process, dynamics, and “potential” have existence and value that do not collapse into the final result. From there it connects physics, the uncertainty principle and dual pictures in quantum theory, the Einstein–Bergson debate about the nature of time and two time axes, and finally moves to means and ends, ethics and Jewish law, including the example of “and he placed it in her hand” regarding a bill of divorce as a definition of action that is not captured only through before-and-after states.
Zeno’s Arrow Paradox: Being at a Place versus Standing Still
The text argues that Zeno asks about a flying arrow: if at every moment it “stands still” at some place, then at what moment does it move, and it points to a standard solution that links the paradox to infinity and differential calculus and to the distinction between points and a continuum. It says there is no need to get there, because the problem is conceptual: Zeno conflates the statement that the arrow stands in a certain place with the statement that it is in a certain place. It defines “standing in place” as a state in which the body is in a place and its velocity is zero, and defines “being in a place” as a state in which it has a position at a given moment even if its velocity is not zero. It concludes that in a photograph with “zero exposure time” you see that the arrow is in another place, not that it is standing still there, and therefore the arrow is moving even though at every moment it has a location.
Velocity at a Point: Calculating through Intervals versus Definition
The text explains that the confusion comes from the feeling that velocity is not defined at a point in time, since velocity is defined as distance divided by time and a point in time has no duration. It argues that in actual physics one gets a function of velocity as dependent on time, so every point in time has a well-defined velocity value, and illustrates this with a parabolic function in which velocity is the derivative. It distinguishes between the way to calculate velocity by means of differences in place and differences in time and taking a limit, and the claim that velocity itself “lives only on an interval.” It says that the claim that velocity at a point is a “fiction” conflates velocity with change of location, because change of location indeed requires a time interval, but velocity means the potential for change of location.
Velocity as Potential and Change of Location as Indication
The text states that change of location is an indication that a body has velocity, but it is not the definition of velocity. It argues that the eyes do not see velocity but locations, and therefore in a point observation there is no visible difference between a stationary body and one flying at enormous speed. It reformulates the answer to Zeno: a body cannot change its location at a point in time, but it can have velocity at a point in time, and therefore “when does it pass” receives an answer in terms of potential at the present moment and not in terms of “passing” that would require change within a point.
Measurements and Velocity: Doppler, Relativity, and Force
The text raises an attempt to say that one can measure velocity at a point in time through the Doppler effect (police radar), where the change in frequency is proportional to velocity, but responds that even there the demonstration and proof rely on intervals and therefore are perceived as a mode of calculation rather than a direct view of “instantaneous velocity.” It argues that this is not a “physicist’s mistake” and that in practice no experimental difference will come out of it, but rather this is a philosophical mistake in conceptualization. It notes that discussion of a gyroscope and an accelerometer leads to the question of whether measurements of force and acceleration are more point-like, and suggests that in the end measurement is done through processes and conversions, but returns to the claim that his disagreement is conceptual, about the definition of velocity and not about instrumentation.
The Uncertainty Principle and Dual Pictures in Quantum Theory
The text suggests that in his article he raised the possibility of explaining Zeno’s paradox through quantum physics: according to the uncertainty principle, if you know position precisely then there is no knowledge of velocity/momentum, and therefore “what is the velocity at the point where it is” is not a valid question in the quantum sense. He rejects this as “a dictionary explained by a dictionary” and proposes reversing the direction: solve the arrow paradox and thereby shed light on the uncertainty principle. He explains that a static snapshot gives position but not velocity, and that to speak about velocity one needs a time interval in which position is no longer defined with full precision, and so one gets a conceptual interplay between precision of position and precision of velocity. He describes a duality between a “position picture” and a “momentum picture” and compares it to “camera glasses” versus “movie-camera glasses,” arguing that the two pictures are conceptual worlds that cannot be “worn together,” and therefore one gets the uncertainty principle and the transition between representations.
Film, Vision, and a Static Perception of Dynamics
The text states that the brain “stitches together” static images into a feeling of motion, and that animated film and filmed motion are built from a collection of frames. It argues that eyes are in that sense a camera that sees a position at each moment, and only from changes in position over time is motion reconstructed, and therefore dynamics are not directly observed but inferred. It uses this to explain why describing velocity through differences over intervals feels natural to consciousness, even if velocity itself is defined at a point.
Velocity without Change of Location: Collision with a Wall
The text argues that a body can have velocity even when change of location is not realized, for example in a collision with a wall with a “completely rigid” body. It suggests that in his language, even at the moment of contact with the wall its velocity is still “100 kilometers per hour,” except that the potential for change of location cannot be actualized in the usual way and so is expressed in other ways such as elastic rebound, heat, or other phenomena. It concludes that this is a relation of cause and effect: velocity is a cause, change of location is a possible effect, and sometimes the effect changes even though the cause exists.
Repentance, Perfection-through-Becoming, and Rabbi Kook: the Value of Potential
The text applies the distinction between potential and realization to ethics and spirituality and argues that “a penitent is preferable to a completely righteous person” because the act of repentance has intrinsic value beyond the result of arriving at a better spiritual state. It presents the possibility that a person repents and does not actually progress “because the yeast in the dough held him back,” but the work itself and the dynamics still carry value even without a state-result. It brings Rabbi Kook on the paradox of perfection and perfection-through-becoming with regard to the Holy One, blessed be He, and argues that the world was created lacking in order to bring into actuality the potential of perfection-through-becoming, so that this becoming is realized through created beings. It connects this to “a higher need,” to “Give strength to God,” to the Arizal at the beginning of Etz Chaim about the desire to bring His names into actuality, and to the motif of actual realization as a fuller perfection, with mention of Anselm as a context for the ontological proof.
Additional Sources for a Higher Need: Jonah, Hoshana Rabbah, Berakhot, and the Lubavitcher Rebbe
The text mentions Jonah and the a fortiori argument from the kikayon plant as a line from which it emerges that the Holy One, blessed be He, “needs us” and not only that we need Him. It brings “Save, for Your sake, our God” as an expression of appeal for the sake of His name, and mentions the Talmud in Berakhot about Katriel and the request of the High Priest to “bless” the Holy One, blessed be He, while noting that Rabbi Margaliot in the encyclopedia of angels cites Saadia Gaon as saying that this is the Holy One, blessed be He, Himself. It quotes the Lubavitcher Rebbe on the portions dealing with the establishment of the Tabernacle as a distinction between the conceptual side and the actual doing, and argues that as long as the thing is not realized, the idea does not come to full expression, in line with “And let them make Me a sanctuary.”
Dynamics in Organizations: the Value of Movement Itself
The text cites sayings from management books that healthy dynamics are good for an organization and interprets them not as the triviality of “arriving at a more efficient state,” but as the claim that movement itself adds value. It uses the image “standing water is not good” to stress that there is value in movement as such and not only in reaching a result. It connects this to the general claim that every process can be described as a function of time, its derivative reveals “potential,” and the question is whether the potential is an arithmetical fiction or an object with independent existence.
Einstein versus Bergson: Static Time versus Duration
The text describes Einstein’s picture in relativity, in which space and time are four coordinates of similar standing, to the point of mixing them and rotating coordinate systems, and instead of speaking about “what happens at time t equals three” one speaks about a “worldline” that describes the entire history. It brings Einstein’s letter to the Besso family as an illustration of a view in which the whole history exists statically and the feeling that time passes is a psychological illusion. It presents Bergson as one who argues for “duration” and for a genuine flow of time and an essential difference between time and space, and says that despite the victory of relativity in physics, Bergson was right on the question of the essence of time. It argues that the move from the language of physics to a philosophical conclusion about the nature of time is unjustified, and that the phenomenological feeling of the passage of time points to a real difference.
Two Time Axes and Time Travel: Static and Dynamic
The text argues that time travel is not only a physical problem but a problem of logic, because the formulation “to be on Tuesday and after that on Monday” requires clarifying the meaning of “after that.” It concludes that in order to make sense of “time passing” and of time travel one must assume two time axes: a static time axis on which the days are arranged, and a dynamic time axis that “flows” over the static axis and can in principle flow forward or backward relative to it. It describes this through the image of a “sawtooth” kind of function in which dynamic time rises and then “goes back” over the static axis, and explains that within this framework it is no wonder that Einstein describes time as space because he deals with the static axis, while Bergson deals with the flowing axis. It mentions Yakir Aharonov and Dario Orovitz and the development of a physics with two time axes, and presents the claim that both laws hold together and therefore Einstein and Bergson are “both right” in different senses.
Means and Ends: the Value of Action beyond the Result
The text concludes that if one sees potential and dynamics as fiction, then the process has no intrinsic value and is only a means of reaching a better static state, and therefore there is no basis for preferring a penitent over a completely righteous person and for conceptions that assign value to the doing itself. It argues that once one recognizes that potential has existence and value, the possibility opens up of valuing effort and action even if the result is not achieved, and the results are an indication of correct action rather than its exhaustive definition. It connects this to a coming discussion about the relation between process and result in ethics and in Jewish law, including a link to the categorical imperative as a point that will appear later.
Giving a Bill of Divorce and Defining an Action: “And He Placed It in Her Hand” versus Edge Cases
The text returns to the topic of giving a bill of divorce and argues that the Sages and Tosafot in Kiddushin seem to define the giving of the bill through many cases because it is hard to capture the definition if one tries to translate a dynamic action into “before and after” states. It argues that the later authorities fail when they define giving as transferring a state from one domain to another, because there are cases in which the end states are not as described and yet there is still a valid bill of divorce, so the definition is not in the states but in the act of giving itself, learned from “and he placed it in her hand.” It says that if the bill of divorce were to “evaporate” from the husband and “be born” with the woman, the end states would exist but there would be no “act of giving,” and therefore the action is not captured by a static description. It ends with the general claim that human thinking is “camera-thinking” and therefore defines dynamics through differences and states, like defining velocity through differences in position and time, whereas in a conceptual world in which dynamics are fundamental the emphasis would shift to integrals and not derivatives.
Full Transcript
[Rabbi Michael Abraham] Last time we started a bit on the issue of means and ends, and last time I talked about Zeno’s paradox of the arrow and the flying thing, and in short what I basically argued was that the paradox really begins from looking at an arrow that’s flying, and Zeno asks: if at every moment it stands in place, at a different point in space, then at what moment does it pass, at what moment does it move between the places? And I said that usually they connect the solution of this paradox to infinity, to differential calculus, and to the claim basically that a segment of time, and of space too, is not built from a collection of very, very dense points—that’s not the right way to look at it—but rather it’s a continuum. Really it’s more correct to describe it, I’m using somewhat rough language here and not completely precise, but more or less, it’s more correct to describe it as a collection of short infinitesimal intervals, if you like, and not of points. The intervals—you can call it an interval of zero length—but an interval of zero length is not the same thing as a point. Meaning, a point has length zero because its dimension is zero, meaning it has no length, not that its length is zero. In an infinitesimal, it’s an interval as small as you want; it’s an interval, it has length, and the length tends to zero, and the zero tends to zero. So the claim is that basically you can’t speak about a point of time because it’s not true that the time axis is made of points. First of all, that’s not true, because you certainly can speak about a point in time. True, it’s not enough, you can’t view the axis as made up of lots of dense points one next to the other, but it’s not true that you can’t speak about a point in time. Of course you can speak about a point in time.
[Speaker B] Just like the number line is also a continuum and you can still talk about a number.
[Rabbi Michael Abraham] It’s the same thing. It’s a representation of the continuum. The number line represents the continuum of time and also the continuum of space. And therefore what I wanted to say is that I think that to solve Zeno’s paradox you don’t need to get into all that at all. The problem lies on the conceptual plane. Zeno is conflating the statement that the arrow stands in a certain place with the statement that the arrow is in a certain place. Those are not the same thing. An arrow standing in a certain place means that in that place its velocity is zero. Meaning: it is in a certain place and its velocity is zero—then it’s standing. But when you say that the arrow is in a certain place, that means it has some position at that point in time, but its velocity is not zero, meaning it has velocity. Even a body with velocity is, at every moment, in a different place; it is not standing, at any moment, in a different place, but it is in a different place. And so where Zeno really went wrong is that he thought that when I look at the flying arrow—say I photograph it with a camera with zero exposure time, a point in time, okay?—then I see it standing in a different place. That’s not true. I see it being in a different place, not standing in a different place. The arrow is not standing. The arrow is moving. And that’s it. That basically removes the problem entirely. What has led people from Zeno until today to get confused by this paradox? I wrote an article in Iyyun on the solution to this paradox, and I looked around a bit beforehand to see, and I was surprised to discover that no one, from what I saw, really offered a solution to this paradox except for the remarks about infinity. That’s the accepted solution. I think they don’t solve it, and it also doesn’t help, because just as with infinity I don’t understand—about infinity I can ask the same question. After all, that tiny interval is also made of points, so what does it mean that it’s made of intervals? It’s made of intervals, each one of which is made of points. You’re just pushing the question one step further. So the question I asked—and I think I also talked about this last time—is: where does this confusion come from? Why don’t people notice that saying the arrow is in a certain place and saying the arrow is standing in a certain place are not the same thing? The claim at the basis of this is that people think the concept of velocity is not defined at a point in time. In order to define velocity you need a segment, as small as you like, but still a segment. You can’t define the velocity of a body at a point in time. And why—what leads people to think that? It’s because we define velocity, we basically define it, as distance divided by time. And a point in space and a point in time have no length; you can’t divide their lengths by one another. You need to talk about distance. Say someone travels a distance of one kilometer in one hour; then his speed is one kilometer per hour, one divided by one is one. Someone travels one kilometer in three hours, in five hours, then his speed is one kilometer divided by five hours, one-fifth of a kilometer per hour, or two hundred meters per hour. And so on. Meaning, basically velocity is defined for us—or at least that’s how we feel, how we think—as a quotient. A quotient of length divided by duration. And a point in time has no duration. And because of that, you really can’t speak in terms of velocity when we are talking about a point in time and space. And so people feel that velocity has to live on an interval, not on a point. Fine—but anyone who’s learned even the ABCs of physics knows that after we calculate the velocity, we have a function that is a function of time. Meaning that at every point in time we have a velocity. Say we have a body moving like a parabola, yes? x equals something times t squared, five t squared. Okay? Then the velocity is the derivative. The velocity of that body is ten t. Never mind right now, that’s just to illustrate. The velocity is ten t. What does it mean that the velocity is ten t? Any t you plug in there, you get some value of the velocity. A t as close as you like to the side will give another value. Meaning that every point in time has a value of velocity, well-defined at every point in time. And if you take another point, as close as you like, you’ll get another value of the velocity. Meaning that the concept of velocity is defined on a point in time, not on an interval. What confuses people is that the way to calculate velocity goes through intervals. What do people answer me when I’ve talked with them about this? They tell me: no, that’s a fiction. There’s no velocity at a point in time. What they mean is velocity over a small time interval around that point. But that’s not true. That’s only the way we calculate velocity. We want to calculate the velocity at a point in time. We have no choice—we don’t know how to calculate velocity except through difference in place divided by difference in time. So what do we do? We take a tiny little interval around that point, see what length it is, divide it by the time it takes to cross it, and that quotient—as the interval gets smaller—
[Speaker B] We become more precise.
[Rabbi Michael Abraham] Exactly. So we reach a limit. And the limit of this process, in the end, is what’s called velocity at a point. But according to that conception, talk about velocity at a point is a fiction. Really the velocity is over an interval, it’s just an interval as small as you like around that point. And I’m claiming that this is not true. I’m claiming that that’s only the way to calculate velocity, but it’s not the definition of velocity. Velocity is defined also at a point in time. And the fact that even if you take an interval as small as you like, at every point in it the velocity will be different, or can be different, okay? So because of that I think this description is not right. Rather what is true is that the operational definition—in other words, the definition of how you calculate velocity—does require getting into intervals of space and time. But the result shows me that this is only a way of calculating. Meaning, in the end velocity is a quantity defined on a point, on a point in time. You don’t need to define an interval in order to talk about velocity.
[Speaker B] Would you say the same thing about time too, that time is also not a concept but distance divided by velocity, say, when we have…
[Rabbi Michael Abraham] No, no. Usually we understand velocity as a derived quantity. Time and place are the basic quantities, and their quotient is velocity. We don’t define time through place and velocity. The symbol v equals x divided by t, but x and t are the basic concepts and v is the derived concept. True, x equals v times t, but no one sees x as being defined as v times t. That’s not its definition.
[Speaker B] Place and time are quantities of nature.
[Rabbi Michael Abraham] Velocity is sort of our definition, something that doesn’t really exist, where you take place and time, which are objective, divide them, and define it. Therefore the fundamental equation is v equals x divided by t, or delta x divided by delta t, and not delta x equals v times delta t. Meaning, that’s just moving terms from one side to the other, but it’s not really—because when we look at the equation here as a definition, then the concept of velocity is what is defined by means of the concepts of distance and time. Okay? Therefore my claim is that the concept of velocity exists at a point in time. Why are people unwilling to accept that? Why does everyone prefer to see distance divided by time as the definition of velocity and not merely as a form of calculation? Because they’re actually not talking about velocity. They’re talking about change of location. And that’s not the same thing. Obviously change of location can’t take place at a point in time.
[Speaker B] Change—it’s a process of change.
[Rabbi Michael Abraham] Yes, that’s obvious. But change of location requires an interval, however short, but still an interval. There’s no change of location at a point in time. The body can’t be in two different places at the same point in time. At that point in time it is in a certain place. Okay? Therefore the concept of change of location really does require an interval. It doesn’t exist at a point in time. But they identify the concept of velocity with the concept of change of location, and that’s wrong. The concept of velocity means the potential for change of location. If a body has velocity, that means that if you wait a moment, you’ll see that it changed location. Change of location is an indication that the body has velocity; it’s not the definition of velocity. If the body changes location, that means that at every point throughout the interval in which you observed it, it had velocity. Because velocity is hard for us to grasp; we really don’t know how to distinguish whether a body has velocity at a point in time. Look—this is the whole paradox of Zeno. Look now at a mathematical point in time. I claim there is velocity there, but you won’t be able to see it. How do we see it? How do we see velocity? We don’t see velocity. What we see is that the place changes, meaning that the body changes its location. But change of location is an indication that the body had velocity. It’s not the definition of the concept of velocity; it’s an indication. If the body changes location, then that means there was a potential for change of location. It’s a potential for change of location. Okay? And therefore my claim is that velocity—the potential—exists at a point in time. Change of location exists only over an interval. That’s the point. And therefore if I now go back to Zeno’s formulation, then I say this: a body cannot change its location at a point in time. That is true. But a body can have velocity at a point in time. And therefore when you ask me when the arrow passes from such-and-such a point to such-and-such a point, at the very moment it is at this point it also has a velocity, which is the potential to be at another point in space at another time. Okay? Therefore it happens at that same time; it doesn’t need to happen somewhere else. When people think about change of location together with being in a place, then really it doesn’t work. When does it change place? But that’s exactly the point—it doesn’t change place. It has the potential for change of place at the point in time at which you’re looking. When you look, you won’t see that. With our eyes we don’t see that a body has velocity. With our eyes we only see the body being at some place. We see it being there, not standing there. And how do we identify that with standing? Only because of this mistake—that if we don’t see that it has velocity, then it seems to us that it doesn’t. But that’s not true. With our eyes we simply don’t see velocities. We see positions. That’s all. The effects of special relativity—can’t you see the velocity even at a single point? Say, length contraction, time dilation, that sort of thing?
[Speaker C] Meaning, you can see at one instant, at a certain point, you can see its length, its…
[Rabbi Michael Abraham] I agree, but that’s a result of it. Meaning there too they’ll tell you that basically you’ll see it as a fiction, because in order to measure length you need an interval of time. You can’t measure length at a point in time. Technically you won’t be able to manage it. I once thought about—not relativity at all—the Doppler effect. After all, the Doppler effect is basically—for example the police radars, how are they built? You send a beam of light with some frequency—not a beam, radio waves with a frequency—it comes back at a slightly different frequency. The difference between those two frequencies is proportional to the velocity of the body that reflected that beam. Now the beam hits the body at one point, hits it and comes back, right? So it seems that I’m measuring the velocity of the body at the moment of impact, meaning I’m measuring the velocity of a body at a point in time. Okay? So there, apparently, you see that the body has velocity, something you can even measure at a point in time. But there too—I don’t even remember now exactly how it worked—I checked this and talked with people. It’s…
[Speaker B] Not true.
[Rabbi Michael Abraham] Why? How does the frequency change then? At a point in time? It hits it and comes back.
[Speaker B] No—what’s the physics, what’s the physical factor that causes the frequency to change?
[Rabbi Michael Abraham] Impact with the body. What do you mean?
[Speaker B] Because there is velocity—the body is moving relative to the wave and doing something.
[Rabbi Michael Abraham] No, there too it’ll be the same thing. If you describe how the Doppler effect is proven—
[Speaker B] It’s not at a point in time.
[Rabbi Michael Abraham] How do they prove the Doppler effect? They prove the Doppler effect like this: when the body moves, you look and see that the spacing containing the number of waves—look at it this way. Meaning, the way to show it is like with the derivative. The way to show it is of course to look at a short interval. But in the end that’s only a way of calculating. The velocity is velocity at a point. So that’s the claim. Fine, I also once talked about this with someone, I don’t remember who anymore, it’s been a few years, and there too I don’t think practically you can show it. Meaning, practically we’ll never manage to see an experimental difference coming out of what I’m saying here. Therefore this isn’t—what I’m saying now is not a physicist’s mistake. It’s a philosopher’s mistake. Meaning, physics won’t change because of what I’m saying here. In any case, the point is that Zeno didn’t distinguish between velocity as the potential for change of location and change of location itself. That’s the point. A remark—maybe one more interesting remark—that in quantum theory, and again let’s just say a word from above, but I think this is an interesting remark for those who know a bit—there are a few here who know a bit. In quantum theory, when there is the uncertainty principle, there are uncertainty principles between several pairs of quantities. Say place and velocity—or momentum, as it’s called in physics—or time and energy, or angular momentum and angle, or whatever—there is an uncertainty principle between certain pairs of quantities. Say time and momentum you can measure together, but momentum and place you can’t. And basically the claim is—in the article I wrote I said that this is actually one option for explaining Zeno’s paradox. To explain Zeno’s paradox not through infinity, not through mathematics, but through physics. Because after all Zeno talks about the question what the velocity of the body is at the point where it stands, at the point x equals two. But there’s no such thing. If you know its position, then it has no velocity—you can’t define the velocity. Quantum theory—that’s the uncertainty principle. The uncertainty principle says that if you know its place precisely, you have no idea what its velocity is. If you know its place with some uncertainty, then there is some uncertainty in the velocity too.
[Speaker B] But at a point, yes, at a point in time—
[Rabbi Michael Abraham] Or at a point in place. If you’re speaking about a point-location of the body, then it has no velocity at all. And that solves Zeno’s problem, because Zeno after all is talking about the question of how—when does it change its place if it is at a certain point. If it is at a certain point, you can’t speak about velocities. Velocity is not a quantity you can talk about when you know the exact position of a body. But when I wrote that as a solution, I said that it doesn’t really solve the problem because it’s a dictionary explained by a dictionary. Meaning, I explain one phenomenon that I don’t understand by another phenomenon that I understand even less. So that doesn’t help at all. Therefore I said there—I did the opposite move. I said: let’s try to understand the paradox, solve the arrow paradox, and by means of it explain the uncertainty principle, not the other way around. And the way—the arrow paradox—if I understand where it comes from, or why it isn’t paradoxical, maybe that will shed light on the uncertainty principle too, which also seems something impossible to grasp. What’s the problem? Why, if a body is in a certain place, is it impossible to speak about its velocity? Now, my claim in light of the solution I offered earlier—I think this really is some kind of explanation of the uncertainty principle. Because basically what it says—what I said earlier—I said that when I look at the body with my eyes, I look at the arrow, then I see the arrow standing at every moment in a different place. Standing—being—at every moment in a different place. Why does it look to me like it’s standing? Because our eyes don’t see velocities. Right? How do we see when a body moves? Only if time passes, meaning only if we see that it really was here before and now it’s here and I understand that it moved, that there was some velocity here, there was some distance that it crossed over time.
[Speaker E] And if I look—well, sorry, sorry—regarding velocities, I said something that Professor Shoham from the Technion studied on this issue. Say, operating human control when the parameter you control—you can control position, you can control velocity, you can control acceleration. It goes through the gas pedal in the car, in the speed of motion, the delta you make—you’re controlling the acceleration, so to speak—but you can’t get to position that way. Not only because there’s a phase lag of one hundred and eighty degrees, but also because a person doesn’t feel that difference. By contrast, control over velocity works. A person controls velocity and it works perfectly.
[Rabbi Michael Abraham] But that’s not velocity at a point—not velocity at a point. You wait an epsilon of time. If you look at a point in time—not a tiny interval, no matter how small, but a point—then the body has no velocity. You see nothing. You see the same body. There is no difference between a stationary body and a body flying at enormous speed if you photograph them at a single point in time.
[Speaker E] First of all, does our eye detect motion? No. Only over time. At the edges of the field of vision. You can do this experiment at home. At the edges of the field of vision you don’t see, and when it starts moving you do see. That’s a property of the brain. It’s a property of an integral.
[Rabbi Michael Abraham] You’re looking at an interval of time. At a point in time you won’t see it, you won’t see velocity at a point in time. That’s a mathematical fact. You can’t see velocity with eyes that are looking at a body at a point in time—they can’t know whether it’s moving or standing still. Rather, you look at a short interval of time, and then fine—that’s exactly the point. Like when we make a movie. How do you make a movie? You photograph a static image and project the images at a very, very high speed, like an animated film, yes? So filmed motion is the same thing. Animation and filmed motion are the same thing. The only difference is that one is a camera and one is a drawing, but the dynamics are produced in exactly the same way. You simply transmit a lot of images, each time with a small change, at high speed, at very high frequencies. Image after image after image, quickly quickly. Then our eye has this kind of fusion, some stitching together of these images, and from our perspective we see it as some continuous process of motion. But really what you have here is a collection of static projections. Why do we need to get to that? Exactly because of this. Because if you look at—we have no way with our eyes to see motion itself. All we can do is reconstruct the fact that there is motion from the fact that we detect a change of place. Meaning, when we look at a moving body, there is a change of place. Because at this moment it was here, and a moment later it’s here, and a moment later it’s here, and so on. Change of place or motion, doesn’t matter—motion of a face or whatever it may be—any dynamic process whatsoever. And then our head already does some kind of integration on it, and as far as we’re concerned it looks as though the body is moving. But really what we see is a collection of static images. At every point we see a different static image. So eyes are a kind of device similar to a camera. A camera freezes the moment, and the eyes each time see the relevant moment, the moment we are in. But eyes are a kind of camera. And what the camera actually sees—even a camera that’s open all the time and sees the body, tracks it moving—it sees it at every point being in a different place. At the next point it is in a different place. Meaning, the mode in which I look at the body is a static mode. I’m basically seeing the position of—right? I have no way to know that it’s moving unless I look, track it over a short period of time, a blink of an eye perhaps, but not a point in time, right? By contrast, therefore the uncertainty principle. The uncertainty principle means that if I see the position of a body at a point, that means I know its position exactly. I have no ability whatsoever to know what its velocity is. And this is not a problem of limitation of measurement. It’s essential. In this kind of viewing, this static kind of viewing of eyes or of a camera, there is no velocity. In this conceptual world the concept of velocity doesn’t exist. You have to expand to some interval in order to begin talking about velocity, and over an interval the position is no longer fully defined, because over the interval it changes place. The moment you increase the uncertainty of the place, you can begin talking about velocities, with certain uncertainties. This description won’t give the h-bar, it won’t give the quantitative size of the uncertainty, but it does give this very interplay between position and velocity. And the reverse too, by the way. Now let’s try to think—thought experiment, philosophical physics. Okay? Let’s try to think of another device, which I’ll call now—the previous device was an ideal camera. An ideal camera is a camera whose exposure time is a point in time. Okay? Now I’m talking about an ideal movie camera. An ideal movie camera is not a movie camera like the ones we know. A movie camera like the ones we know is basically a collection of successive photographs. It’s basically a camera that I use repeatedly at dense successive times. An ideal movie camera is a movie camera that looks at a body and knows its velocity. Let’s say there were such a thing. We can’t—our eyes don’t work that way. But there could be some creature from outer space that comes down here and its sensory system is different from ours. It looks through glasses that are… A person like that, when he looks at a body at a point in time, he’ll see that the body is moving, but he’ll have no idea where the body is standing. He won’t be able to talk about the body’s position. That’s the principle of the uncertainty principle. I’m now projecting from our world—we don’t understand how the perception of that person is built. But I’m saying that just as for us there is an uncertainty principle between place and velocity, for him too there is. Only for us—what’s the difference between us and him? Both of us are subject to the uncertainty principle. Only our sensory system is a kind of camera. And his theoretical sensory system—I don’t know whether there are such creatures, but in principle—his sensory system is a movie camera. Okay? So when he films a movie, he doesn’t need to take a collection of continuous snapshots and then stitch together those discrete images. Rather from his perspective he sees the image—the opposite. He… the Doppler meter doesn’t see stationary bodies.
[Speaker E] What? The Doppler meter doesn’t see stationary bodies.
[Rabbi Michael Abraham] Yes, exactly, it’s the same principle. And when he wants to talk about location, he’ll have to define it; he won’t understand what you’re talking about. For him, the basic concept would be velocity, not location. From his point of view, location is the integral of velocity. From our point of view, velocity is the derivative of position. From his point of view, location is the integral of velocity. But that’s a definition. In other words, velocity is the basic quantity, and location is something he can calculate. But in order to calculate it, he’ll again have to look at an interval, do some kind of integration, okay, in order to talk about location. So there’s really a kind of duality here. A fictional creature—again, I have no idea whether such a thing exists. But in principle, such a thing could exist; there’s nothing preventing there from being such an abstract creature.
[Speaker E] Inertial navigation is based on the fact that I have an accelerometer; integrating that gives me position, and an angular velocity meter, right, a gyro, whose integral gives me my angular position. And that’s how an inertial navigation system works.
[Rabbi Michael Abraham] Yes, but the question is again: when you integrate velocity, how do you measure the velocity itself?
[Speaker E] The velocity itself is measured by means of the gyroscopic effect.
[Speaker B] You measure acceleration, not velocity.
[Speaker E] No, with a gyroscope I measure angular velocity because…
[Rabbi Michael Abraham] How do you measure angular velocity?
[Speaker E] How do I measure angular velocity? I’ve got a gyroscope there that is fixed to the plane or the ship or whatever it is. Okay. And I prevent it from keeping its place in space by applying forces to it that oppose the precession forces, and I measure those forces, and I know that I’m applying them with an electromagnet. Fine, but how do you measure the speed of the gyroscope? No, angular velocity. I measure the angular velocity of the body that is moving the gyro. And also with the gyroscope, linear velocity is one integration; I get the velocity.
[Speaker B] You integrate twice. You measure acceleration, integrate once and that’s velocity, once more and that’s…
[Rabbi Michael Abraham] How do I measure acceleration? I don’t measure it through velocity; I measure force.
[Speaker B] Ah, you measure force. Of course. That’s what you measure in an accelerometer too—you measure force.
[Rabbi Michael Abraham] Ah, that’s an interesting point, because that really is measurement at a point.
[Speaker B] You measure force.
[Rabbi Michael Abraham] And then in principle…
[Speaker B] You measure force and you have mass, and then you have acceleration, and then you integrate once and that’s velocity, once and that’s…
[Rabbi Michael Abraham] Measuring acceleration through force—that, there’s no problem measuring pointwise. With velocity there is a problem.
[Speaker E] Okay, no, now I measure velocity through force on a mechanical gyro, and with an optical gyro… an optical gyro is basically built so that a beam of light from the same laser is split into two beams, one goes clockwise and the other counterclockwise, reflected by three or four mirrors… that’s a laser gyro, it’s a gyro…
[Speaker B] Fiber optic, which is…
[Speaker E] Those are technical details, that’s not important here.
[Rabbi Michael Abraham] Technical details—my only question was whether, in order to measure angular velocity, you’re not actually using a derivative. You look at what angle it’s at now, and a moment later what angle it’s at, and divide.
[Speaker E] No, I measure the force required…
[Rabbi Michael Abraham] Okay, you’re talking about the mechanical one and not the optical one.
[Speaker B] Exactly, so that’s acceleration.
[Rabbi Michael Abraham] Yes. Fine. Acceleration can be measured pointwise. Angular. What?
[Speaker B] Angular acceleration, it doesn’t matter.
[Rabbi Michael Abraham] Angular acceleration, linear acceleration, there’s no…
[Speaker E] No, I measure angle—the gyroscope wants to preserve its place in… and how do you measure that? I don’t let the gyroscope do that; I do keep it fixed to the body, but the force…
[Rabbi Michael Abraham] The force required to keep it there is proportional to the angular velocity. That’s the claim. Ah, okay. Yes, that’s interesting. And that too is apparently a pointwise measurement.
[Speaker B] You always measure force.
[Rabbi Michael Abraham] Yes, so I’m saying that if I measure force, that’s a pointwise measurement; that really is interesting.
[Speaker C] Why is measuring force pointwise?
[Rabbi Michael Abraham] Because in principle force is defined at a point. By the way, when you measure force, how do you measure force? I think through accelerations. How do you measure…
[Speaker C] Acceleration?
[Rabbi Michael Abraham] You—exactly, that’s why I’m saying—you apply electr… that force meter basically accelerates electrons. And the acceleration of the electrons is proportional to the force. I think in the end force measurement is also done through measuring acceleration. Fine, but now we’re really getting into instrumentation. In any case, so the claim—the claim I want to make here,
[Speaker B] Why, why—you put in a spring? And you see how much it compresses.
[Rabbi Michael Abraham] Then that’s surely displacement.
[Speaker C] So then you’re back to measuring velocity.
[Rabbi Michael Abraham] Not exactly. No. Because how much it compresses doesn’t mean you have data about when exactly its length was what at a given instant. You’re not taking differences over different times; at any given time you see the difference from its phi length—yes, its relaxed length. That’s a pointwise measurement. Fine, never mind, that’s really not our issue here. What I just want to say is—I’ll just finish the quantum remark. In quantum theory it’s known that every pair of non-commuting quantities—that is, quantities between which there is an uncertainty principle—basically creates two kinds of picture. There’s the momentum picture and the position picture. You look at the world through the glasses of velocities. And I ask, say, what happens to a body when it has this velocity, and what happens to a body when it has that velocity. That’s one kind of question. Those are questions I ask in the language of velocities, in the language of the momentum picture. There is a dual way of looking at the same reality, where I ask what happens to a body when it is at this place, and what happens to a body when it is at that place. That’s a dual perspective. These two perspectives don’t talk to each other. And every pair of quantities that stand in an uncertainty relation also has two pictures: the energy-and-time picture, the position-and-momentum picture. Now, according to the interpretation I presented here, that’s obvious. Because the uncertainty principle basically comes from the fact that when I put on glasses—or eyes—camera glasses, then I see positions. In order to see velocities, I have to take off those glasses and put on movie-camera glasses. Then I see only velocities and not positions. With the first glasses I see the position picture; with the second glasses I see the momentum picture. That is exactly why there is an uncertainty principle, because these are two different pictures, two different conceptual worlds, and I can’t wear both pairs of glasses together. Either I see the world through these glasses, or I see the world through those glasses. In other words, the fact that the uncertainty principle gives rise to two pictures that don’t talk to each other—I think that is exactly a reflection of the explanation I suggested here. That the relation, the relation between velocity and position, is really the relation between viewing the world through a camera and viewing it through a movie camera. Therefore the position picture and the momentum picture are exactly the expressions of the uncertainty between position and velocity. Okay, I’m closing the parenthesis on that remark regarding quantum theory. So let’s get back to our plane. The claim is that in the final analysis, what I want to say is that velocity has a meaning beyond change of position. It is a potential for change of position. And in the end, last time I think I even gave the example—an example or examples of this—that there can be a situation in which a body has velocity, but that velocity does not manage to go from potential to actuality and cause a change of position. For example, when a body crashes into a wall. Okay. Physicists say that the moment it is already touching the wall its velocity is zero. But that isn’t intuitive. Because after all it had a very high velocity, let’s say, and the moment it touches the wall, suddenly what happens there? So what is its velocity at the instant of contact with the wall? Again, you can say that as it approaches, it goes down. But no—it’s pointwise, let’s say a completely rigid body. A completely rigid body is pointlike, elastic. Okay. Then something very strange comes out here. And what I want to claim in this language is that when it touches the wall, its velocity is still a hundred kilometers per hour. Even when it touches the wall, its velocity is a hundred kilometers per hour. The fact that it has velocity cannot come out in the form of a change of position. Unlike a regular situation, where velocity is a potential that goes from potential to actuality through the body changing position, here the body cannot change position; the wall stops it. Since the wall stops it, that potential expresses itself in another way. If it’s elastic, then it goes in the other direction, or it gives off heat, or all kinds of things. In other words, it comes out in other forms. That potential comes out in other forms. In other forms. That potential comes out differently, and that is the indication that the relation between velocity and change of position is not the simple relation we’ve been talking about until now, because there can be a situation in which a body has velocity and that will not be expressed in a change of position. In other words, it has the potential to change position, but that potential does not go from potential to actuality. And that is precisely the indication that velocity and change of position are not identical; they are not two identical things. Rather, one is the cause and one is the effect. The fact that you have velocity is a cause of your changing position. Okay? They are not identical to each other; it is cause and effect, and therefore sometimes there can be a cause and the effect will be something else. The effect won’t be that, but for other reasons it will be something else. And I said—like—I gave the example of Rabbi Kook’s problem of perfection and perfecting with regard to the Holy One, blessed be He, where he says that one of the perfections is to perfect oneself. Human beings, who are lacking in their essence, can perfect themselves. And the Holy One, blessed be He, who is perfect, cannot perfect Himself. And if He cannot perfect Himself, then one of the perfections is missing from Him; He is supposed to be complete in all possible perfections. And self-perfection is also one of the perfections. I started with the statement that a penitent is preferable to a completely righteous person. “A penitent is preferable to a completely righteous person” means that the value—or the value that exists in repentance—is not only that it brings you to a spiritually better state, to be more righteous; rather the very act of repentance is itself a value. Besides, of course, the fact that you also reach a spiritually better state. But let’s say you repented and did not advance in your spiritual state—does that have no value? No, it has value. You are a penitent even though your spiritual state did not improve. For some reason it came out in the form of heat, because you had the potential to advance spiritually but it didn’t manage to go from potential to actuality. So it came out—the wall was there, let’s say—you didn’t manage. So fine, you did the work, you did the work and didn’t manage; the leaven in the dough held you back, you didn’t succeed. Do you deserve something for that? In other words, did you advance spiritually? The answer is yes, because the work, this dynamic of repentance, has some value even if in the end the result—that I become more righteous—is not achieved. Okay? And that is the claim, and therefore a penitent is preferable to a completely righteous person. I said: at most, a penitent can reach the state of a completely righteous person, so how does he become more than a completely righteous person? The answer is because he has the value of self-perfection, not only the fact that he becomes complete. Even if he becomes completely complete, that is being righteous plus this added thing, that he is also perfecting himself, whereas the righteous person is not perfecting himself. And then Rabbi Kook argues that our whole world, which was created lacking, was actually created in order to bring out into actuality the potential for self-perfection that is found in the Holy One, blessed be He. That is, the Holy One, blessed be He, has all perfections, including the perfection of self-perfection. But the self-perfection found in the Holy One, blessed be He, is the potential to perfect Himself; He cannot become more perfect, because He is already perfect. So He has a potential to perfect Himself; there is, as it were, a wall that stops Him—it’s not a wall, but there is something that means it cannot go from potential to actuality; He cannot be more perfect than He is. So how can He bring that potential out into actuality? He simply creates us, creates a world with lacking creatures, and imposes upon us the obligation to perfect ourselves. When we perfect ourselves, we are essentially bringing out into actuality the potential for self-perfection that exists in the Holy One, blessed be He. Therefore He is, as it were, perfected through us, and this is the secret of “a need on high,” and “Give strength to God,” what the Ari writes, yes? That we give power to the Holy One, blessed be He; He needs us. I brought Jonah, right? That a fortiori argument of the castor-oil plant. We spoke about that, I think, right? And there too you see that the claim is that the Holy One, blessed be He, really needs us; it’s not that we need Him. He really needs us. Without us He will not be able to perfect Himself. And that would be a problem: He has the potential for self-perfection, but that potential cannot go from potential to actuality. And we are here so that this potential can go from potential to actuality. That’s what the Arizal says at the beginning of Etz Chaim: that the Holy One, blessed be He, created the world because He wanted to actualize His names. That is, He wanted to actualize—within Him there already was, in some potential sense, all the ideas that exist in the world. But there is some value—and this is connected to Anselm—the value of actual realization is more perfect than something that is only an idea, that is, a concept. If something is realized, it is more perfect than if it is only an idea. That is the assumption of Anselm’s ontological proof, never mind for those who know it. And here, basically, there is the same claim of the Arizal. He is essentially saying that although the Holy One, blessed be He, has the potential for self-perfection, if that potential does not go from potential to actuality, then apparently that potential still does not express full perfection. Even though the perfection lies in the existence of the potential, not in actual progress, still it has to progress in actuality in order for the potential apparently to have full value, and therefore He needs us, basically.
[Speaker B] Another possible example of this: all of Hoshana Rabbah is basically “save us for Your sake, our God.”
[Rabbi Michael Abraham] Yes, there are many other places. “Give strength to God.” What? The Holy One, blessed be He, needs us. That’s what the Talmud in Berakhot says, with the song by—what’s his name—Avraham Fried, “Bless me,” yes? But Rabbi Margaliot in the Encyclopedia of Angels talks about Katrial—yes, I saw Katrial there. So he says there that this means the Holy One, blessed be He Himself; it’s not an angel. He brings Rav Saadia Gaon there. Rav Saadia Gaon writes that, that it is the Holy One, blessed be He Himself. And that is the straightforward meaning of the Talmud. And then it means that the Holy One, blessed be He, asks the High Priest to bless Him. That means He needs him; that means that if the priest does not bless Him, then He Himself is not complete, meaning He needs the blessing from below in order to bring Him that thing.
[Speaker D] The Lubavitcher Rebbe says about the portions dealing with the erection of the Tabernacle—why are there several portions? So he says: the first portions are the conceptual side; the Holy One, blessed be He, conveys to Moses what He wants, what is supposed to be. And after that, the actual doing.
[Rabbi Michael Abraham] As long as it isn’t realized, the idea is not fully expressed.
[Speaker D] “And they shall make Me a sanctuary”—they shall do, actually do the thing.
[Rabbi Michael Abraham] Okay, so that’s really the weekly Torah portions, you’re saying. Yes. Nice. In any case, another example of the matter: there are statements like this, for example in management books, where they say that dynamism is healthy for a factory, for an organization. Okay? Now, what does it mean that dynamism is healthy for an organization? The simple or simplistic conception says: obvious—if you’re not in a complete state, then become more efficient, reach a more complete state, and then that will be good. That’s not what the statement means. Because that would basically be a trivial statement. Obviously, if you can reach a more optimal state, that’s better. The statement that dynamism is healthy for an organization means that movement itself is healthy for the organization, not because the movement will bring you to a more efficient state, but because the very fact that you are in motion itself apparently gives some added value to the organization. Which in the end may also show itself in results, because you can’t…
[Speaker B] Talk without results, but stagnant water is not good. Stagnant water is not good. Yes, exactly.
[Rabbi Michael Abraham] So I’m saying, yes, but in the end it’s not good because it stinks. In other words, in the end it is still the state of the water. But the point is that it’s because it’s standing still. Yes, exactly. But the point is that I need it not to stand still, not in order for it to get there. In other words, it’s not that I want it to have velocity so that the velocity will be realized through the realization of the potential. That’s not the point. Rather, there is something in the potential itself that gives me added value. And that is exactly this statement. It basically means that there is something in motion, some added value in motion itself, not only as a potential for change of place, whereby only in that way I can improve, change place. And every such dynamic process. In other words, whenever something changes, you can describe it as a function of time and differentiate that function. Once you differentiate that function, what you have discovered is the potential of that change. And the potential of that change—you can now discuss whether that potential is a fiction, whether what really exists is only the different states and you define a derivative as some kind of fiction, or whether you say no, I have basically discovered or exposed here some object that also has independent existence, a potential that is actualized in the way we see, in the dynamics we see. But the potential has independent existence; it is not a fiction that merely describes the fact that we are changing place or changing state. Perhaps a continuation of the same issue—and with this I’m more or less finishing with the physics matters, or actually not, because there’s another section, maybe not today. There is a very well-known dispute between Einstein and Bergson. Henri Bergson was a French Jewish philosopher. Between Bergson and Einstein regarding the nature of time. Einstein, in the theory of relativity, essentially presents a picture in which space and time are four interchangeable coordinates. You have length, width, and height, say, three spatial axes, and one time axis, and all events in the world are described in terms of those four axes. Now it’s not only that—that was true even before Einstein, to describe things as a function of place and time. With Einstein, these axes have the same status; they can even be transformed into one another. In other words, you can rotate the coordinate system, but not only of space, also with time. And then what will happen is that you get a new system in which, say, axis number two is a combination of space axes and time axes. Each axis is a combination, and then space and time get mixed with each other; they’re the same thing. It’s not—before Einstein, and also with Galileo and Newton, there was the energy or the potential of position, the potential energy of the body, as a function of position and as a function of time. It’s a function of x, y, z, and t, place and time. That was before Einstein. What Einstein… that was not yet with Galileo and Newton. Meaning, a four-dimensional space in the sense that you can even rotate the coordinate system; in other words, time and space are the same thing. And therefore, in Einstein’s theory of relativity, they don’t speak at all about an event as a function of time—there’s no such animal. What they talk about is a world-line, that’s what it’s called. There is a world-line, meaning that you describe a body by describing its whole history. For example, if you want to describe the location of the body, you construct, say in one dimension, so you have x and t here on a two-axis system, okay? A body described in relativity is an entire line on that axis system, what’s called a world-line. That line describes where it was at every time. Okay? At constant velocity in special relativity, it’s a straight line. Fine, never mind. Now the body is not—that is, relativity doesn’t look at the body in terms of what happened to it at time t equals 3. There’s no such thing. In special relativity you won’t find such a thing as t equals 3. What you have is how one looks at the time axis and how one looks at the space axis—contraction, expansion of the time axis, the space axis. But “where is the body at t equals 3” and “what is it doing when it gets to x equals 5”—that does not exist in the language of special relativity. Rather, you look at the world-line of the body. And if there is, say, a system moving relative to that body, then the world-line changes angle. Okay? The description is always a global description, where the body means the body across all space and time; it is not a body at a point of space and time. That is Einstein’s basic description. And then the claim is—this is the well-known expression about it, part of Einstein mythology—that when his friend named Besso died, he sent a letter of condolence to Besso’s family and told them: look, the truth is that we physicists know that nothing happened. Because in the end Besso is defined from the moment he was born until the moment he died, and it was always true that Besso would be born in 1920 and die in 1960, let’s say just for the sake of discussion, okay? So what difference does it make that right now we are in 1960? When we were in 1950, wasn’t it also true that Besso would die in 1960? It was also true. So what difference does it make where we are relative to ourselves or relative to Besso? In other words, this sounds absurd because it imports relativity into psychology. But in relativity, that really is how things are viewed. You look at the whole biography; you do not look at a point in time, and so the whole biography never changes. That is the biography, that is the person, it’s a completely static picture. And therefore Einstein basically claimed that time is static. This feeling that time passes is a psychological illusion. The whole business, basically—the history exists in its entirety all the time, always in the same form. But what is the history? The history is from the Big Bang until infinity, that is the history, not a point. This decomposition into points is a psychological effect that should be ignored; in other words, that’s psychology, not physics. Physics does not speak in that language. And Bergson objects to this. He claims that there is duration—time as duration. This is a very basic idea in Bergson, that time is made of durations, not of points. It is not static; rather time flows. Time is different in its essence from space. The fact that time flows and space is static, okay? There was a dispute between them; I think they never met, but there was this indirect controversy. It was known that there was some disagreement between Bergson and Einstein, and of course Einstein won easily, because relativity simply conquered the world. But I think he was mistaken—Bergson was right. In other words, the point is that in relativity that really is the description. The question of what time really is—that is a completely different question. He thinks that everything we feel is psychological effect, an illusion. Physics describes reality itself. That is not at all clear to me. On the contrary: the feeling of the passage of time tells me that there is something different about time than about space. Why do I feel time differently than space? Because time flows, as Bergson says. And the fact that you choose to describe it as a world-line because that is the physical constraint or the physical language you chose—which of course is brilliant and successful and everything is wonderful—but it is a language. Only a language. Why infer from that what time and space really are, or that they really are the same thing? Why? Where does that leap from physics to philosophy come from? Then my claim, and I continued this claim, was that in the end this is a more complex picture. They are both right, essentially. And what happens is, in order to understand this, one has to think about popular science-fiction movies and also physicists. Yakir Aharonov is very fond of this issue, deals with it quite a bit, and he is a physicist from Tel Aviv University. And this basically concerns the question whether one can go back in time or cannot go back in time. I once wrote a column on the website about this. There was someone in Herzliya, what’s it called there? The college there, the Interdisciplinary Center in Herzliya. And there was someone there in computer science or something who “solved” the problem of time travel, that’s how they presented the nonsense there. And he made some kind of simulation; he built software that manages to represent time travel. Yes, how does it do that? I no longer remember, but I think this is how it does it—and if not, then this is what it should do. You basically define two time axes, where one time axis is static and the second time axis can flow forward or backward over the first time axis. Or in another language I’ll put it this way: another physicist from Tel Aviv University, a close friend of mine, Dario Orovitz. Dario Orovitz is a very nice Jew, a returnee to religion, really nice, amazingly sweet, also taught me at Bar-Ilan; later he moved to be half at Bar-Ilan and half at Tel Aviv. And he, together with various students over the years, developed all of physics under the assumption that there are two time axes and not one. And the claim is that this solves various open problems in physics. Okay. Now at some point I had some idea and I went to one of his students and said to him: look, the truth is I can explain why—why there are two time axes. It’s not only that it solves problems in physics, but what the rationale behind it is. I explained it to him. After I explained it to him he said: good morning, Elijah—in the very first article by these guys, that’s exactly what they explain. I hadn’t read it, but that’s where they start from. And the point is this: when you talk about time travel, the problem is not a problem in physics, the problem is a problem in logic. Going back in time is impossible not because there is some physical constraint that doesn’t let us go back in time, but because it isn’t defined. What does “go back in time” mean? To go back in time means to be on Tuesday and after that to be on Monday. After that when? Wednesday. Wednesday. On Wednesday to be on Monday? I didn’t understand—am I on Wednesday or on Monday? If I’m on Monday I can always be on Monday, no problem at all. On Tuesday I can be on Tuesday—not only can I, I will always be on Tuesday. On Tuesday I will always be on Tuesday. On Monday I will always be on Monday. What does “go back in time” mean? Going back in time does not mean being on Tuesday and then being on Monday. Going back in time means being on Tuesday and after that being on Monday. Because being on Monday before that is no problem; rather, after Tuesday being on Monday. But what does that mean? If I’m after, then I’m on Wednesday. You mean that on Wednesday I’ll be on Monday? If I’m on Wednesday, then you just explained to me that I’m on Wednesday; what does it mean that on Wednesday I’m on Monday? What is that—making a square triangle? What is this thing? If you are on Wednesday then you are not on Monday, and if you are on Monday then you are not on Wednesday. What is this thing? Or I’ll formulate it differently: when we talk about the feeling that time passes, okay, as opposed to space which is static—what does “time passes” mean? Think about it for a second—how do you define this concept at all? What nonsense. What does it mean, “time passes”? When I say that a certain body moves, it means that it changes place along the time axis. In other words, look at the point t = 1: at time t = 1 it is at this point, in this place. At t = 2 it is in this place. In other words, place changes along the time axis. But when you say that time passes, you want to claim that time changes along the time axis? After all, when something changes, when something passes, that is always done along the time axis. And to say that time itself passes is a meaningless concept—passes over what? This lies at the base of that same question, by the way, that I said earlier, this question of time travel. Why? Because both of these questions imply that apparently, in order to speak in that language, we need to define two time axes. There is one time axis which is a standard time axis—not going back, not flowing, nothing—it is static. Fine? There is a second time axis that passes over it.
[Speaker B] That first one is Einstein’s.
[Rabbi Michael Abraham] Fine, we’ll get there in a second. And there is a second time axis that passes over it, and therefore it is called flowing. What does “flowing” mean? The second time flows over the first time. Okay. And now I ask myself whether it is possible to make it flow backward. Now what does “flow backward” mean? That I should be on Monday after I was on Wednesday? The answer is yes, yes. After I was—that is, after I was on Wednesday on the static time axis, I will arrive at Monday on the dynamic time axis. The static time axis always goes forward; that is, I advance along the axis of static time, but when I measure where I am in terms of the dynamic axis, I suddenly find myself backward. Suppose you draw time—let’s call it a diagonal line.
[Speaker E] Like the train one? What?
[Rabbi Michael Abraham] Yes. That’s the picture in space, and I’m talking about time. So look at a graph of flowing time over static time. Fine? What I basically want to say is that there’s a sawtooth here. The flowing time, the time that flows over the static time, flows all the time at constant speed and then suddenly drops downward. That is called going back in time. At that time point I go back, I drop to an earlier time on this axis, and then it keeps flowing onward. That is basically two axes. Okay, and one can be described as a function of the other, no problem. You can talk about the speed of its flow, negative speed of its flow, no problem—it’s like space. Now it’s no wonder that time for Einstein is like space, because he is talking about time that flows over the second time. In other words, the point is that when you talk about static time, you are talking about Einstein. When Einstein talks about static time, he really is talking about time made up of points, not durations. It is time that stands still; it doesn’t flow or anything. But when Bergson talks about dynamic time, he is basically talking about time that flows over static time. And therefore, it may be that they are both right. There are two time axes: an Einsteinian time axis and a Bergsonian time axis, and therefore what we feel, that time passes, is not a psychological illusion. It is simply this feeling that there is a time passing over our internal time axis in some sense. Okay? Therefore we are actually perceiving another aspect of reality. It is not necessarily a psychological illusion. That is the claim. Then one says that there are two time axes, one dynamic and one static, and Einstein and Bergson are two laws and both are right, essentially. That is the claim. Fine, enough with the physics amusements, but what I now want to say is the following claim: if I sum up this introduction that I gave, it is that if I really see the potential for change as a fiction, then there is no room to speak about the value of the dynamic itself. There is no such thing as the dynamic itself; that’s a fiction. The dynamic is only a means in order to reach a static state. A state is by definition something static, better. To be a penitent. If I do not see the act of repentance—if I see the act of repentance as a derivative, as a fiction—then basically you need to be as righteous as possible. You need to aspire to be righteous. Okay? How do you progress? Of course the aspiration to be righteous is the engine that makes you progress, but it itself is not really something of value, it has no reality of its own; it is only the way one progresses. The goal is to be in a better state. Then indeed a penitent is not preferable to a completely righteous person—that’s Rabbi Abbahu and Rabbi Yohanan there, who is preferable. So if a penitent is not preferable to a completely righteous person, at most he will become a completely righteous person. But if you understand that this potential is not just a fiction—there is a movie camera here, not only a camera—this potential has existence in its own right. True, it is also a potential for changing state, but besides that it is also itself something one can relate to, something one can give value to. Then the possibility opens up—not necessary, but at least possible—to see some kind of value in this thing itself as well. Then being a penitent, or being in the dynamism of an organization, what I spoke about before, you can now say that this is not only a way of describing the fact that you are improving, but that the improvement itself, even if it does not come out in actuality as an improved state, a better state, is itself something of value, itself an advantage. So this depends on not understanding things like Zeno. In other words, the claim that there is value in the process, not only as a means of improving the state, actually obligates us to adopt a non-Zenonian picture. Because Zeno understands that velocity is a fiction; basically what exists is only a state, or velocity is a change of states. We define a fiction in mathematics; we differentiate the function. Okay, but basically velocity is a change of state, and therefore he claims that velocity exists only over an interval and not at a point in time. Velocity at a point is a fiction; we simply calculate over an interval around that point. All these perspectives basically say that velocity is not a potential for changing state. Velocity is a fiction that we define as a potential for changing state; there is no such thing really. What really exists are only the states. And if the states change, we define a function called the derivative function, but that is our fiction. It does not represent something in reality itself. If indeed we are in Zeno’s picture, one cannot speak about the process as something valuable in itself. By contrast, if I see this not as a fictitious calculation but as a way to arrive at a quantity that really has a correlate in reality—in reality itself, velocity has meaning. A person with an ideal movie camera, with cognition in the form of a movie camera and not of a movie camera—he won’t see velocities at all; for him place is a fiction, an integral of velocity. Okay. Therefore the fact that I am built in the form of eyes is simply because that’s how I’m built. But it’s not really that location has real meaning and velocity is a fiction. Both have real meaning. The form of my cognition is the question of what I am observing through. Okay?
[Speaker C] With a sonic boom, do you hear velocity? With a sonic boom you hear the velocity of the plane.
[Rabbi Michael Abraham] Right, I hear a consequence of the velocity, not the velocity itself.
[Speaker C] Isn’t that pointwise velocity?
[Rabbi Michael Abraham] It’s a consequence, so I’m not sure that question is even defined. Because it’s a consequence of the velocity. You’re asking whether it’s a consequence of pointwise velocity, and then that takes us back to all the Doppler stuff like we talked about before. It’s the same thing. Okay? Because it’s not the velocity itself; the boom is created from a consequence of the velocity. If the plane flew in a vacuum, there would be no boom. So my claim, basically—this whole introduction basically says that when we go on to talk about means and ends, or about actions and results—we’ll also see this identification—then we need to define action as not just some fictitious way of describing the achievement of a new state, where what really exists in the world is only the new state. No. Action has existence in its own right, to judge it by that. In other words, action has value regardless of its results. The results are an indication that the action is a correct action; that will bring us to the categorical imperative—we’ll get there too. But the result is an indication that I performed a correct action. Besides the fact that maybe the result also has value—I also—but not only. There is also some aspect in which the result is an indication; that is, the fact that I changed position is an indication that I had velocity. And the value in my movement is that I have velocity, not that I change place and arrive at a better state. That is basically the claim. From here on I’ll try to speak a bit about the relation between the process and its result, between the means and its result, and look at morality, also Jewish law, in various such places. But I think this is the philosophical background needed in order even to be able to talk about this question. There’s another thing—before that, not long ago we spoke about giving a bill of divorce, I don’t remember even in what context that was, one of the recent classes I think. We talked about why the Talmud, Tosafot in Kiddushin perhaps, why the Talmud…
[Speaker C] Tries to…
[Rabbi Michael Abraham] To define the giving of a bill of divorce through lots and lots of cases instead of giving me the definition itself. And my claim there was the same thing. In other words, the giving of a bill of divorce, basically—that’s what made the whole thing click for me—the passage in tractate Gittin, that’s where the whole idea fell into place for me. I wrote the philosophical article in Iyun after I learned that passage. My claim was that the reason the later authorities can’t manage to define the giving of a bill of divorce is because they’re trying to define the giving of the bill of divorce through what the situation was beforehand and what the situation is at the end. To say that she acquires it, or that I transfer it from my domain to hers. And then they say, wait a second, but if it doesn’t pass into her domain, there’s still a valid bill of divorce in this or that case, so that’s not a correct definition. And that definition gets challenged each time through other situations where it’s not the first state A and the second state B, but something else. But my claim is that state A and state B are really both unnecessary. They’re an indication that a certain kind of action is required. You’re trying to capture it through the edge states—what was before and what will be afterward—because you’re looking at it through static glasses, through a camera. But really what the Sages are trying to tell me is the concept of velocity. The giving of a bill of divorce is an action. It’s an action such that before the giving, the bill of divorce is with me, and after the giving, the bill of divorce is with the woman. But it’s not that if the bill of divorce, say, evaporated from me and was born with the woman, she would be divorced. Because there was no act of giving here, even though the initial state was as the initial state should be and the final state was as the final state should be. Because the initial and final states here do not really constitute the essence of the definition of the thing. What’s needed is “and he shall place it in her hand”; from that the Talmud learns the point that there has to be giving. What does “and he shall place it in her hand” mean? Not that in the end it should be in her hand, but the very act of giving itself. How do you define an action? And the understanding is that we, with our always-static mindset, grasp things statically, both in thought and in perception—we grasp what is static. Therefore, when we define dynamic processes like actions, we always define them through the state before and the state after. And that’s what wrecks the whole thing for us; that’s why we can’t get to the definition. Because you can’t define it through a state of before and after. It is defined as a dynamic process, and each time the before and after may be different, but it will still be the same dynamic. You can travel at the same speed and that will take you from x equals three to x equals five, but it will also take you—or from minus three to minus one. It doesn’t matter; it’s the very same speed, even though the before-state and the after-state are different states. So if you understand that the thing I’m trying to capture is something dynamic, then you understand why it’s impossible to describe it through before-states and after-states. And all our attempts to define it are always in that form. We don’t know how to define dynamics. There’s no way to define dynamics except through a cropped perspective. That’s why we also define speed through the difference in positions divided by the difference in times. That’s our definition of speed; we have no other way. We’re stuck with the mindset of a camera and not a movie camera. And therefore every dynamic concept will always have to be translated, for us, into differences between static states. A derivative, basically. In a world where speed or dynamics is the fundamental quantity, there would be no derivative at all. In other words, you wouldn’t need differentiation; you’d need integrals, but not derivatives.
[Speaker B] So here you need to grasp it that way.
[Rabbi Michael Abraham] Yes, there’s a relation here between speed and position, of what kind of dynamic to grasp. From dynamics and up, you won’t encounter derivatives.