Mysticism – Lesson 3

[Rabbi Michael Abraham] So actually, as Shlomo reminded us, we’ve basically reached a certain problematic tangle. Because on the one hand, when I tried to define the concept of mysticism, I refused to ground it in false things or in error. Mysticism is not necessarily—that’s not what defines the concept of mysticism. Even someone who thinks it’s all mistaken, and even someone who doesn’t believe any of these things, I don’t think that’s the correct definition of the concept. It has a categorical definition. Now we can start discussing whether I accept it or don’t accept it. And the categorical definition was something whose path of access is not given equally to everyone, something esoteric, subjective, however you want to call it. After that I moved to the plane of: okay, so still, how does the mystical explanation or description relate to the ordinary, simple description? So I said that here I started entering the analysis of parallel explanatory planes. And I brought several examples of this, I’m not going to repeat them, but the conclusion in the end was that when we offer two different explanations for the same thing, it can be one of two possibilities. Either neither of the two explanations is itself really an explanation—that is, neither constitutes a sufficient condition for what is being explained—and only the combination of the two explanations together actually provides the sufficient condition. I said that an explanation has to be a sufficient condition for the result, so only the combination of the two explanations together is really an explanation. We call each one an explanation, but that isn’t really accurate. I gave the example of someone leaving religion or someone returning to religion, whichever. You can explain those steps on the psychological plane: the person underwent a crisis, went through some sort of shock, and therefore is looking for a different path for himself; and there’s a philosophical explanation that says that the person arrived at different conclusions from what he thought until now. Now, as I said before, if, say, the psychological explanation were really an explanation, then it would have to be a sufficient condition. And a sufficient condition means that if the shock occurs, there will be a change of path even if he doesn’t find any philosophical justification for it, because that’s what a sufficient condition means: that its presence is enough for the conditioned thing to occur, for the event or thing being explained to occur. And the same thing if I think the philosophical explanation is an explanation—then that means the philosophical explanation is a sufficient condition. That means that without any crisis and without anything, the person ultimately takes that step because he reaches different conclusions. Anyone who reaches different conclusions changes his path—that also, of course, isn’t true. So apparently the more balanced way to look at this is that when a person takes such a step, it’s a combination of the two planes, the psychological and the philosophical. And each of us—it varies in different proportions, and each time the proportions are different, and each person has different proportions—but in principle you can look at it on the psychological plane, you can look at it on the philosophical plane, but someone looking for a sufficient condition, meaning an explanation, will have to use the combination of the philosophical plane and the psychological plane together. Only both of them together can provide a sufficient condition for the result. For example, a person goes through a shock, so he wakes up and reexamines himself: is the way he lives or the way he thinks right or not? And then he starts checking—maybe there are things that seem more compelling to him—so the shock caused him to examine, but the examination itself is ultimately carried out using philosophical tools; he’s looking for what seems true to him. And therefore, in fact, only the combination of psychology and philosophy together can give us some kind of full explanation, an explanation in the sense of a sufficient condition, for the phenomenon we’re discussing. On the other hand, if we’re talking about two explanations each of which is a full explanation, meaning one that provides a sufficient condition, that can’t be. Because if both explanations are each a sufficient condition, then that means if explanation A holds, that’s a sufficient condition, so the thing being explained will happen even though B did not occur; and if B occurred, then even though A did not occur, the thing being explained will also happen, because B is a sufficient condition. But that can’t be. Meaning, then one of them is the explanation. The second one is not an explanation. Okay? Or alternatively—it’s possible to say that either A happens or B happens. That can also be some kind of combination. Meaning, either-or. But it can’t be both-and. It can’t be that this is an explanation and that is an explanation. There can’t be phenomena where, if it’s a sufficient condition—not a necessary one, but a sufficient one—then either A or B; that too is a possible model. Say, for example, I want to explain why fire was created. So it could be either striking a match or concentrating the sun’s rays with a magnifying glass. Right? Either one of those, if it happens, there will be fire. That’s a sufficient condition. Fine? And each of them can be an explanation, but not both together. Meaning, the fire happened either because of the concentration of light, the sun’s rays, or because of striking a match. It can’t be that both explanations are true together. Meaning, that this event is explained both by explanation A and by explanation B, and A and B, each by itself, is an explanation—that is, a sufficient condition. So that can’t be. Now, why am I saying this? Because when we now approach our topic, which is mysticism, and we want to understand the relation between a mystical explanation of certain phenomena or certain things and another explanation—scientific, rational, whatever you want to call it—a different explanation, an exoteric explanation, say, as against hidden or mystical—then what can the relation between the two be? Of course you can say that the mystical explanation is simply an incorrect explanation. But I said: I do not identify mysticism with what is incorrect. Even if you may think that mysticism is always wrong, that’s still not the definition of mysticism. The definition of mysticism is something else, which we discussed. So that means there ought, in principle, to be at least a possibility of a double relation to the same set of facts or events or principles. There could be a mystical explanation and an exoteric, rational—or however you want to call it, objective—explanation, and both would count as explanations. Yes, that’s really the point. Except that if indeed each one by itself provides an explanation, and not only their combination—notice, if it’s the combination of both then there’s no problem; we’ve gone back to the example of the person leaving religion or returning to religion. But if we insist on a model in which each one is a full explanation in itself, then that can’t work. The only way to allow such a state of affairs is only if these two explanations are translations of the same explanation into different languages. Right? When I explain a scientific event in Hebrew and explain it in English, those are not two different explanations of the same event. It’s the same explanation presented in two different languages. One is a translation of the other, but they are not two explanations—they’re one explanation. Meaning, the only possibility for there to be two full explanations, both of which are also true—not either-or, but both this is true and that is true—is only if those two explanations are basically translations of one another, which really means they aren’t two explanations; it’s one explanation just presented in two languages. I’ll explain what I’m getting at before moving on. The example I’ll of course get to later is, say, a kabbalistic explanation and an exoteric explanation of verses in the Torah, of Jewish laws, of whatever. There is an exoteric explanation and a hidden explanation. Now the claim is that the exoteric explanation is a full explanation in itself, and the hidden explanation is also a full explanation in itself. Meaning, you can look at Torah, or Jewish law, or whatever, through the lenses of the hidden, and you can look at it through the lenses of the revealed, and each set of lenses gives you a full and coherent picture. Right, this is that belief in Pardes. We talked about the fact that the Torah can be explained on several different planes simultaneously: plain meaning, hint, homiletics, and secret. But even within the plain meaning there are several explanations, and within the secret there are several explanations, but there are several parallel explanations, each of which is a correct explanation. Now this can’t happen, as I said before, unless those explanations are translations of one another. If I assume that the hidden explanation is not a different explanation from the exoteric one, but is only formulated in a conceptual system or in a language called hidden, then that basically means that the hidden is not really something parallel to the exoteric but identical with the exoteric—just formulated in a different language, like speaking in Hebrew and in English. So if, for example, Abraham our forefather and Sarah are translated into philosophical language as matter and form, and I translate them into kabbalistic language as kindness and strength, okay? Or the right side and the left side. Or judgment and mercy, yes? Or something like that—mercy and judgment. All kinds of things like that—if each of these offers a full interpretation or a full explanation of the Torah, of those portions, say, of Abraham and Sarah, then that means that what we have here is really translation. Meaning, it means that matter and form translate into kindness and judgment in kabbalistic language; in philosophical language it’s matter and form. So basically that means—it kind of empties the concept of mysticism or of Kabbalah of content, because it basically means that it’s only a translation of the revealed into another language, into a different conceptual world—but it’s a translation, it’s saying the same thing in another language.

[Speaker C] You could say it in both directions.

[Rabbi Michael Abraham] What? I can’t hear.

[Speaker C] You could say it in both directions. Either it empties Kabbalah of content, or it empties the revealed of content.

[Rabbi Michael Abraham] The opposite seems more plausible, right? So I’ll also get later to the issue that the Ba’al HaLeshem, for example, comes out very sharply—one of the greatest Ashkenazi kabbalists who lived in Jerusalem, was connected for years with Rabbi Kook, and was Rabbi Elyashiv’s grandfather—he came out very sharply against kabbalists who saw Kabbalah as metaphor and not as an objective description of spiritual worlds. For example, Hasidism—or at least major currents in Hasidism—tends to see Kabbalah as some kind of metaphor for the human soul. It’s just another way of relating to inner spiritual-psychological phenomena within us. Okay? And that basically says exactly what I said before: that grasping the hidden as a translation into a different language of the revealed means it isn’t saying something else; it’s saying the same thing, just in a different language. The Ba’al HaLeshem argued that such a thing is not Kabbalah. Such a thing is psychology in another language. But he argued that Kabbalah means dealing with something else, not dealing with the same thing in a different language. Therefore his claim was that Kabbalah deals with spiritual worlds. There is some kind of correspondence between the human soul and spiritual worlds, but that is only a correspondence. The subject Kabbalah deals with is spiritual worlds. Therefore it deals with a different subject; it is not dealing with the same thing just in a different language. Okay? That is basically his claim, because otherwise you’re not studying Kabbalah, you’re studying psychology. That’s basically his claim.

[Speaker E] Does that explain the people who opposed Kabbalah, like the Dor Daim among the Yemenites? They opposed the whole concept of…

[Rabbi Michael Abraham] Why would one need to oppose Kabbalah because of that? What’s the problem?

[Speaker E] No, because for them it doesn’t fit their worldview. Because if it’s only the same thing in a different language, then okay. But they argued that all of Kabbalah is something that…

[Rabbi Michael Abraham] I’m not familiar with their objections there, but on the face of it I don’t see why one would need to oppose it, whether it’s a metaphor or a description of facts.

[Speaker E] Maybe they opposed it because there are concepts there of, like, anthropomorphism—an arm, hands, things like that, no?

[Rabbi Michael Abraham] Maybe because of that. It could be. But then in any case I think that even if it’s a metaphor they could still oppose it; the metaphor still anthropomorphizes the Holy One, blessed be He. So I don’t know, I’m not familiar with the background of that opposition there, so I don’t know how to answer that. But on the face of it I don’t see, specifically in this approach—whether metaphor or not metaphor—a basis for opposition. What difference does it make? Anyway, that’s the point. The claim is that we’re basically in a tangle here. If we want to claim that the mystical and the exoteric, or Kabbalah and the plain meaning, are both full descriptions of the facts—call it the Torah portions or Jewish law or whatever—but also mysticism dealing with the world as against science, for example, they too are basically full descriptions of reality, whether in mystical language or scientific language—this cannot be true unless they are translations of the same thing into different languages. And as we said before, that basically empties one of the two sides of this equation of content. So there aren’t really two things here. I want to make a different claim: that these aren’t the only two possibilities. There is something in the middle, and I think that’s the more correct model for explaining the relation between mysticism and non-mystical thought. First I want to illustrate such mappings or translations into different languages just to clarify more what’s at stake. So let’s start, for example, with a case that many people are very fond of: the innovation of Copernicus. Yes, until Copernicus, cosmology was based on the idea that the earth is at the center and the universe revolves around it, the planets and the sun revolve around it. And Copernicus changed the point of view and basically proposed that the sun is the center and the planets, including the earth, orbit it. Now it’s common in the world to think that Copernicus discovered some scientific fact that had not been known until his time. I deny that. I think Copernicus discovered nothing. Copernicus simply proposed a different point of view on the same set of facts, a different coordinate system. Instead of describing our cosmology with the center of the coordinate system—the origin—sitting on the earth, let’s place the center of our coordinate system on the sun. Even though these are ellipses and not exactly circles, I’m ignoring that point right now. So I place the center of the coordinate system at the sun and it turns out the description comes out much simpler. Or in other words, I want to argue that the question whether the earth revolves around the sun or the sun revolves around the earth is a meaningless question. Both answers are equally correct. There is no either-or here; these are just two ways of describing. Choose a coordinate system. If you place it on the earth, then the sun revolves around the earth. If you place it on the sun, then the earth revolves around the sun. Yes, it’s simply a matter of point of view. There’s no truth and non-truth here. Copernicus’s innovation was that the point of view that places the center on the sun creates a picture that is much easier to describe. Instead of getting tangled up with epicycles and deferents, you get a much simpler picture, so why not change the coordinate system in a way that gives us a simple picture? But it’s not a more correct picture. There is no more-correct and less-correct here. In physics there are major debates connected to Mach’s principle, for those who know, and all kinds of such things, about how far one can really define objectively who revolves around whom in the physical sense. But in the kinematic sense, meaning simply in the sense of defining motion, there is no doubt that there is no truth and falsehood here; both are equally right. Copernicus did not discover a truer truth than what came before him; both are equally right. Yes, very often religious thinking is accused of being rigid like pre-Copernican thinking. And people are convinced that Copernicus discovered America. Copernicus discovered nothing. Copernicus did not discover any scientific fact; he discovered a convenient coordinate system. That’s all. He discovered a coordinate system in which it is more convenient to describe our cosmology, our astrophysics. So I use this example to show you that two descriptions that seem very, very different—one of them is even much simpler than the other, the Copernican description is much simpler than the other—are actually translations of one another. These are not two forms of description; this is using two languages to describe the same thing. And therefore many times there are two things that seem very different to us, but when we dig a little deeper we may discover that what we have here is actually translation. Last time I also gave the example in physics of teleological and causal descriptions. Right? I can describe optics or mechanics as a set of teleological laws, purposive laws: the body wants to reach the place with the lowest potential energy, the lowest potential. That’s a purposive description—wants to get there, strives, as it were. And the causal description is that the force of gravity pushes the body downward. These are two equivalent descriptions. In the end one can say that this is a translation of the same description into two different languages, even though the languages are completely different. Someone who looks at them superficially won’t discern any connection at all between them. But it turns out this is simply translation. You can prove that everything said here has a counterpart there; you can translate every description here into a description there, and it turns out that these are simply two languages, not two explanations or two descriptions but two languages of the same description. And therefore, certainly with respect to the hidden and the revealed, there are such claims. I think many people think this way: that this is basically only a translation. It’s simply a translation. Therefore, for example—yes, this is how it’s commonly said, I don’t know whether there is a source for it or what the source is—but it is commonly said that the Ari, of blessed memory, relied on Maimonides in Jewish law, and generally followed Maimonides. Now Maimonides is perhaps almost the most prominent figure in his alienation from kabbalistic thought. So it’s strange that the most quintessential kabbalist—some would say the greatest of the kabbalists—would adhere in Jewish law דווקא to Maimonides’ rulings. And I think the claim underlying this is that if Maimonides’ mind worked correctly in the revealed sphere, then he will arrive at the correct result. Why should I care if he explains it in the language of the revealed? In the calculation of the hidden as well, in the end, that is apparently the correct Jewish law. Just do the calculation correctly. And if you trust Maimonides to do the calculation correctly in the revealed, then take his result and you can rely on it in the hidden as well, because it is basically the same thing. So why should I care that he’s doing the calculation in another language? Okay, this is a very common way of relating to the relation between the revealed and the hidden, and as I said before, it basically empties one of these two sides of content, because it means these are two different languages for describing the same thing. So what difference does it make?

[Speaker F] Rabbi, it matters because there’s a difference between languages in the sense that some things are easier to formulate in a certain language.

[Rabbi Michael Abraham] One hundred percent, good. So I’m saying: if, as I said before with Copernicus, you come to the conclusion that it’s easier to formulate it that way, then fine. I don’t think that in cases where there are parallel explanations in the revealed and the hidden, one of them is simpler than the other. Certainly not systematically. I don’t think kabbalists would tell you that looking at things in the hidden is always simpler than looking at them in the revealed, or vice versa. I don’t think that’s the claim. They claim that this is the correct outlook, and those of the revealed will claim that that is the correct outlook. So that’s not what distinguishes them here—not simplicity. So we need to understand what does.

[Speaker G] So Rabbi, if the revealed and the hidden are two different forms of the same thing, how can there be dispute between them?

[Rabbi Michael Abraham] Hold on, we’re getting there. You’re getting ahead of me a bit; I’ll come to it.

[Speaker E] Halakhically? Yes, there is. For example, Maimonides—let’s say Maimonides holds that one puts on tefillin on Hol HaMoed, and according to Kabbalah that’s like cutting down the saplings.

[Rabbi Michael Abraham] One second, we’ll get there, we’ll get to everything. Look, the clearest example of these things—and I’m just moving here to Wikipedia—is a coordinate system. Okay, a coordinate system. So we’re used to the system—look at this thing here. Look at it as if there’s a set of axes here. Okay, this is the y-axis and this is the x-axis. Right? So let’s say this point that’s here, the point that’s here. Okay, so you can look at it: its x-component is here, and its y-component is here, right? You can describe it in terms of x and y, its projection onto x and its projection onto y. That’s the Cartesian coordinate system. Cartesius is Descartes, yes. Descartes’ coordinate system; he found it, he invented it. But there’s another form of description called the polar form, which means I describe this point not by means of its projections onto the x-axis and the y-axis, but in terms of its distance from the center and this angle here between this line and the x-axis. That too is a unique description of this point.

So let’s take, for example—the circles here are radii of one, two, and three. Let’s take, say, the circle of radius two. Okay, this point that I looked at before, this point here, is an angle of sixty degrees, it says here, right? An angle of sixty degrees means that if this thing here, the radius here, is two, right? That’s the radius of the circle. So it’s two. Then this thing here is two cosine sixty, which is exactly one. Cosine sixty is one-half. So this is one, okay, the projection onto the x-axis. And this thing here is of course square root of three, okay, by the Pythagorean theorem. So y is square root of three, x is one, and this thing of course is two by the Pythagorean theorem. So you can describe this point in two ways: the Cartesian form is to say one, square root of three—its x-component and its y-component. And you can describe it by distance two at an angle of sixty degrees. That too will bring you exactly to this point in a unique way. This is called the Cartesian and polar description of points in the plane. You can describe it in Cartesian form, you can describe it in polar form. These two descriptions are completely equivalent.

You see—whoever knows this, and even if you don’t, it’s pretty clear, it’s known. Right? I can get—here I have x,y, that’s the Cartesian description. r and theta—r is the radius, the distance, and theta is the angle. You can get there: if you have x and y, you can find r and theta; if you have r and theta, you can find x and y. Okay, all in all, familiar things. Why am I showing this? Because this is a wonderful example of two different descriptions in completely different languages, but really what’s going on here is a translation of the same thing. After all, these are just points in the plane. You can describe them in Cartesian language or describe them in polar language, but these are translations. It’s a translation of the same thing into two different languages. So you can’t say—you can’t ask, for example, what’s real, the Cartesian description or the polar description, which is more real. What does “more real” mean? These are simply two languages for describing the same thing; there’s no right and wrong here.

That’s exactly like Copernicus’s description. Okay? Basically Copernicus’s description tells me—the question is always polar—the question is whether I place the origin of the axes on the sun or on the earth. That’s all. Other than that, they’re two equivalent forms of description. And of course there are infinitely many coordinate systems; you can formulate as many as you like, and they’re all equivalent to one another. So this—these are two examples, Copernicus and the Cartesian and polar coordinate systems—these are examples of descriptions that seem different, but really when you look more closely you understand that they’re simply translations of the same thing. A translation into different languages of the same thing.

Maybe another example I once thought of: the periodic table in chemistry. Okay? The table lists the elements there—it doesn’t matter—a list of elements that are basically the basis of all matter known to us in the universe. Okay? A series of a certain number of elements. In ancient physics—let’s call it metaphysics or ancient physics—they built the whole reality of the world on four elements: earth, water, air, and fire. Earth, dust, whatever—water, air, and fire. Okay? And every object or every creature, every object in our world, is some mixture of those four elements.

Now, to us this sounds like some kind of ancient physics completely detached, of course, from observation and quantitative, systematic, scientific thought. And so again, as with Copernicus, it’s obvious to us that they were talking nonsense and that today we know what the truth is. But I want to claim that even there it isn’t so simple. Because you can definitely define water, earth, air, and fire as certain combinations whose different mixtures really can describe every object in the world. Say, I don’t know, a stone has a great deal of the earth component and maybe a bit of the water component, and therefore it’s some kind of—yes—a vector with four places, and in each place you put the intensity of earth, air, water, or fire that there is in this thing. Right? Every such thing is basically a vector of four components. So you can describe every object in the world in this language. You can’t say that this description is wrong. Aristotle—I don’t think Aristotle meant to claim that—how do you make a stone? You take earth, water, and fire in a certain mixture, mix them well, and out comes a stone. He didn’t mean to say that. He meant to talk about the properties of the stone. The stone’s properties are that it has some kind of inertia, it has some kind of heaviness like dust, but it isn’t dust in the sense that it doesn’t scatter, because it’s rigid, so maybe there’s also a water component here binding the dust together and making it into one thing. It doesn’t matter right now; I’m not an expert in Aristotle’s metaphysics. But that is a completely legitimate and valid way of describing all the objects in the world.

Nothing here turned out to be false. It’s simply perhaps an unproductive form of description: you can’t produce chemical substances from it, or perhaps predict the outcomes of chemical processes. The fact that modern chemistry is much more productive, much more useful, lets you predict many more outcomes, explain many more things with it—that’s why it’s clear to me why we adopt it. But understand that in this sense this is exactly like the reason we adopt Copernicus’s coordinate system. It’s not because it’s truer; it’s because it’s more effective, useful, efficient, elegant, simple, convenient—whatever. But there’s no right and wrong here. It’s just a different coordinate system, and you can describe reality with it and with that other coordinate system. There’s no problem with that; there’s simply nothing false here.

And from this perspective you can see—yes, we’re almost reaching postmodernism. From this perspective you can see that basically every description you give of reality is as correct as any other description. It simply uses a different conceptual system. Choose some different basis, and different combinations of the basis elements will give you the objects or the principles you want to explain. Choose a basis, and it will give you the descriptions, that’s all. If you want to describe this in terms of the properties of earth, air, water, and fire—fire rises upward, water flows, earth rests but crumbles, air flies, I don’t know, is thin, whatever. Different combinations of thinness, heat, heaviness, tangibility, massiveness—different combinations like that really do describe all the objects in the world. That’s true, and so there’s no problem describing things that way; it’s just apparently not scientifically effective, it won’t get you very far. You won’t be able to explain many things with it, or predict many things, or use these things technologically. Because I think they didn’t get very far in pharmacology on the basis of Aristotle’s four elements, while on the basis of the periodic table they apparently do better, okay, in producing medicines. So fine, it’s more useful, more effective. Is it more true? I don’t know if it’s more true. It’s simply looking at the same thing from a different angle, that’s all.

In a certain sense maybe you can even say that it’s looking at the same thing at higher resolution. If we were to analyze the components of fire—the chemical components, as it were, of fire—yes, there’s no such thing, but the chemical components of fire or of dust or of air or something like that, maybe we would arrive at the periodic table. And then these are simply descriptions at different levels of resolution, that’s all. Not right and not wrong; it’s not a question of right and wrong.

[Speaker H] Wait, Mikhi, how many dimensions do you need to describe reality? I can’t hear. How many dimensions do you need to describe reality perfectly?

[Rabbi Michael Abraham] What does “perfectly” mean? You can describe it in as many dimensions as you want; it depends on what interests you. If you want to describe reality at the level of whether something resembles fire, air, water, or dust, then you have a full description with those four components. The question is what you’re trying to describe in reality. If you want to describe for me chemical compositions in what we call them today—how exactly something is formed and what it does—then Aristotle won’t help you much, yes, that’s obvious. Okay?

[Speaker H] So it’s not similar to Copernicus, where it’s identical. No,

[Rabbi Michael Abraham] I agree.

[Speaker H] It’s not.

[Rabbi Michael Abraham] It’s not similar to Copernicus, where it’s a transformation. I agree, it’s not similar to Copernicus in that sense—let’s put it this way: I can probably describe Aristotle’s four elements using our chemistry and physics today, that’s pretty clear. But I can’t build our chemistry and physics today on Aristotle’s earth, air, water, and fire. So they’re not mutually symmetric, unlike Cartesian and polar coordinate systems, where it’s two-way.

[Speaker B] So it’s not a translation? What? It’s not a two-way translation.

[Rabbi Michael Abraham] Right, so that’s why I’m saying—you’re right that it’s not exactly the same as the Cartesian and polar coordinate system. But all in all I want to claim that there’s no right and wrong here—that’s the point. It’s a translation at least in one direction. Okay? So the claim—what I want to say—is that there are things that on the face of it look very different, like what you see with Kabbalah, say, and the revealed layer, but when you look deeply it’s certainly possible that both are true, both describe the same thing in different languages, that’s all. So there aren’t really two different explanations or two different modes of relating. But notice—I’m returning—

[Speaker I] back to Wikipedia, and here there’s a very interesting point. Look at this equation, yes? For anyone uncomfortable with equations, it’s not really necessary. But what happens when x equals zero?

[Rabbi Michael Abraham] So if x equals zero, this expression is undefined, right? Right, undefined. And it’s true that arctangent of infinity isn’t such a disaster—you can assign something to it, that’s ninety degrees—but if you look at when both y and x equal zero, then it is certainly undefined. And what does this thing mean? Look at this point in the center. Okay, this point in the center—its Cartesian description is x equals zero and y equals zero. Its polar description is r equals zero because the distance from the origin is zero, any sigma—well, any angle you want, any theta. Right, any angle you want; the angle is undefined. Or if we draw it—look, maybe I’ll do it, sorry for the drift into mathematics, mathematics really helps clarify the point here.

[Speaker I] Look, let’s say this is a coordinate system, but now I’m going to do the following exercise: I’ll draw a Cartesian coordinate system where this is r and this is theta. Okay? Now I ask: when x equals—

[Rabbi Michael Abraham] zero and y equals zero, that’s a point on the system—yes, if this were x and y then the point x equals zero and y equals zero would be here, right? What does this point correspond to on this plane?

[Speaker I] It corresponds to the entire y-axis, right?

[Rabbi Michael Abraham] To r equals zero and every theta. It corresponds to an entire line in the polar plane. A point in the Cartesian plane corresponds to an entire line in the polar plane. In other words, r has—in short, when we want to identify a point in Cartesian coordinates with a point in polar coordinates, it doesn’t work in one place. At the point x equals zero and y equals zero, what corresponds to it is not one point in the polar description but infinitely many points. What is that infinity? r equals zero and any theta you want—infinitely many thetas. Okay? That means that this correspondence, even though it looks very one-to-one and you can pass from one to the other—not true, it breaks down. There’s a point where there is no correspondence. One point in the Cartesian description does not have one corresponding point in the polar description; it has an entire line in the polar description. This causes what in topology are called topological defects, and that’s an amusing subject in itself, but I won’t go into it here.

But what this actually means is that what looks to us like a simple translation of one into the other is not such a simple translation. You can’t translate the point x equals zero, y equals zero into polar language in a simple way. There are infinitely many ways to describe that point there. The translation breaks there. And when the translation breaks, that means that after all it isn’t merely one translation of the other; these are two different languages. There’s a close connection between them over the overwhelming majority of points in the plane, but at one point—or along one line, if you look at the polar side—it breaks. There the translation doesn’t work. And when the translation between two languages doesn’t work, that means these are not just two different languages but they really describe two different things. Except that they are identical to each other in almost all contexts, apart from these topological flaws, these defects.

And it turns out that there are correspondences that are supposedly translations of one another—they are translations of one another, but it turns out that they’re not completely translations. It looks like a translation because for most words in the language there is a translation of a word here against a word there, but if you wanted to write the dictionary entry for x equals zero, y equals zero in the polar dictionary, you’d need a whole book for it—not a book, an infinity, you couldn’t write it. There is no translation into the polar language, and that means that there’s something here that is—I don’t know whether to call it not a translation—two different things that in some senses still are translations of one another, but apparently not completely, not essentially.

[Speaker H] But that’s irrelevant. So say it’s different, even though it’s similar, but it’s not a sufficient condition. Either it’s sufficient or it’s sufficient. I didn’t understand. Okay, so the transformation from Cartesian to polar isn’t perfect. Okay. But as a sufficient condition, by definition, one is enough.

[Rabbi Michael Abraham] Okay, that’s exactly the point. So I’m saying: at every point in the plane except the origin, both are sufficient conditions. Give me the Cartesian or the polar, and I have the full information. At one point, no. At one point, no.

[Speaker H] But in the definition of a sufficient condition that isn’t relevant.

[Rabbi Michael Abraham] No, it is relevant. Because what I actually want to claim—what I’m now going to want to claim—if you remember from the previous lesson, I spoke about a miracle and the relation between a miracle and a scriptural decree, that both are really topological flaws. Both are breaks in correspondences, yes? What is a miracle, for example? A miracle is, say, the splitting of the Red Sea. The Holy One, blessed be He, here—the Jewish people are standing on the shore of the Red Sea. Right now I’m assuming that there really was a miracle there in the simple sense, yes? Leave aside the other explanations for now. So the Jewish people were standing on the shore of the Red Sea; physics does not provide the response that the Holy One, blessed be He, wants. Right? A sea doesn’t just split in two, or into twelve, on its own. So physics doesn’t work. What does the Holy One, blessed be He, do? He stops physics, intervenes, and performs a miracle. Now the event that happened there has no explanation in physics, because the laws of physics were suspended at that point in time. But it does have an explanation on the theological plane, on the plane of the Holy One’s calculations. He did it for some reason, apparently a good reason that He had. Okay?

So that means that physical explanations and theological explanations may perhaps be almost translations of one another. Every event can be explained physically, like Newton’s apple, and you can explain it theologically. But sometimes it breaks. There are points that have an explanation in the hidden realm but have no explanation in the revealed realm. The correspondence between the hidden and the revealed breaks. That is the miracle. Or if you want: a scriptural decree is basically a topological flaw in the correspondence between the revealed and the hidden. Right? Because with a scriptural decree, what it means is that here there is a law that has no explanation in the revealed realm. If it has no explanation in the revealed realm, then why was it done? Apparently there is some good reason why the Torah states this law. The accepted assumption is that there is—again, I’m assuming the accepted assumptions for the moment without getting into ideologies about what people really think; I’m only illustrating the principle, the idea.

So the claim is that this law probably has an explanation in the world of the hidden, in the theological world, in the world of the Holy One, blessed be He. In our mode of thought, in our everyday life, it has no explanation, or at least we don’t know the explanation. So the correspondence between revealed explanations and hidden explanations breaks in these laws of scriptural decree, just as the correspondence between science and theology breaks in places of miracle. What does that actually mean? It basically means that mysticism relates to the revealed the way polar relates to Cartesian—but notice, like polar and Cartesian once we’re a little smarter and understand that the relation between polar and Cartesian is not just a simple translation. There’s something else here. There is a correspondence perhaps in very many contexts, but there are places where it breaks.

Look, let me give you, for example, an illustration that may help make a little clearer how this can happen. There’s Douglas Hofstadter’s book Gödel, Escher, Bach—a very famous book, it won a Pulitzer Prize, I think, for that book. And there he tries to explain foundations of logic, computability theory—yes, certain foundations of mathematical thought and computer science. And among other things he proposes a game. And this game—I looked it up by the way—it has a Wikipedia entry, it’s called the MU puzzle, MU puzzle, but on my screen it comes up backwards, I don’t know, this Wikipedia entry is written… Hofstadter’s golems must have abused that entry, because something there comes up strangely, somehow left to right, and I couldn’t figure out why. I wanted to share it with you, but it didn’t display properly.

In any case, the principle is this: he proposes the following game. Let’s suppose we have a language with three letters: M, I, and U. Okay? Now we start with the word MI. We have four—I think there were four rules there—certain manipulations that one is allowed to perform on a word, on an existing word, in order to produce another word that is legal in the language. So for example, if the word MI is legal, and let’s say there is a rule that anything beginning with M—you can double everything after it. So then the word—wait, one second. Okay. Fine—

[Speaker I] We have an alphabet, an alphabet of three letters. All right?

[Rabbi Michael Abraham] That’s the alphabet of the language. Think: instead of twenty-two letters in Hebrew, there are three. Now we have one word that is legal. We are given that the word MI is legal in the language—call it an axiom, okay? Now we have three rules, or four rules, that tell us what you may do to a word that is a legal word in the language in order to generate another word. That is called the grammar of the language. Okay? So let’s say that a word beginning with M—fine? Let’s say the first rule, I’m just making this up; his rules were something like this, I don’t remember exactly, I told you I couldn’t get the Wikipedia entry to display. Let’s say this is the first rule. That means that from the word MI, according to this rule, you can generate MII, right? You can double the I, because that’s what’s there. But if this word is legal, then now this word is also legal, right? Because you can now double the II, because that also begins with M, and so on. So that’s one rule.

Let’s say a second rule is: for a word ending in I, you can replace—you can add U. Okay? That’s the second rule. So for example, this word, if it’s legal, then this word is also legal. Okay? Or if this word is legal, then here too you can add U. Okay? Now notice: now this word is also legal. Now look what I generate from it: I generate this word, and I double everything after the M according to the first rule, okay? And so on. And now you see how the dictionary of this language expands. You can add here, of course, that when a word has two U’s, you can delete them both. Just for example, it doesn’t matter right now. So if I have some word with two U’s, then I can delete both. Fine? Or whatever, some set of rules. This is the grammar of the language. That set of rules generates the dictionary of the language. Fine?

Now Hofstadter’s claim—the question he asked—was: suppose I’m given the set of rules. Can one—can the word… is the word MU legal? Or prove whether it is legal, or if it’s not legal. Can you prove, on the basis of the first word—the given word that is legal—and, let’s say, the three rules—again, these aren’t his rules, so I’m just saying this, don’t try to solve it now, it’s not the right puzzle—but just to explain the principle. Yes? Will I succeed in reaching the word MU? Fine? That was the question. When you start playing with these rules, you discover that it’s very far from simple to prove that this word is legal or not legal.

What Hofstadter does is say: okay, now let’s look at that same system of rules and translate it into the following language.

[Speaker D] Yes, sorry, a translation. Now, M is translated as three, I is translated as one, and U—

[Rabbi Michael Abraham] is translated as zero. Okay, it doesn’t matter. Now notice that the word MI, for example, is thirty-one in the new language, right? If M is three and I is one. But now I can translate the rules too. Now notice what I’m going to do. A word beginning with M means a word beginning with three, right? So basically you can double everything after the M. Or let’s start with: a word ending with I is a word ending with one; you can add U to it. What does that mean? Multiply it by ten, right? Add one more zero. Let’s say thirty-one ends with one; you can add zero to it, so we move from thirty-one to three hundred and ten. That means you can multiply it by ten. When a word has two U’s, you can delete both. What does that mean? If they’re at the end, say, then you can divide by a hundred. If not at the end—say, if it has two U’s at the end, you can delete both, meaning you can divide by a hundred.

You see that I can translate the rules, the grammatical rules, into arithmetic language. In other words, instead of formulating typographical rules, rules about letters, once I turned it into numbers it became a mathematical problem. And now the question is whether I can produce thirty from thirty-one. Can I produce MU? MU is thirty. Now you understand that you can give this to a computer program or prove it using mathematical tools. If you have this set of mathematical rules, you can prove that from thirty-one you cannot reach thirty in any way. Why? Because, for example, if you start with thirty-one, you’ll never get a word divisible by ten. You can show from the rules that you will never have a word divisible by ten. You understand that this opens up completely different possibilities for dealing with questions, with puzzles, with checking the legitimacy of a word. Now I can do it in mathematical language. All I did was translate the letters into numbers. That’s all. But suddenly the whole game becomes a different game.

But notice: it’s not really a different game, it’s just a translation into another language of the same thing. You see that this is once again an example of two systems that seem on the face of it completely different. If I had presented you with this puzzle and then presented you with the puzzle in its mathematical form, it would have looked like two completely different puzzles. It’s the very same puzzle, just a one-to-one translation.

Okay, but now I’ll take one more step forward. And now look. Suppose—I return to our page—up to this point I’ve shown only what is called translation, two different things that look different but really can be translation. Now I’ll show you how translation can break. Let’s take, say, as an example that we built the whole dictionary of this language. Suppose it’s a finite number of words, it doesn’t matter right now; we managed to build the whole dictionary of the language. Okay? Now I want to think about another set of rules that would generate exactly—would generate exactly—the same dictionary. Suppose there are ten thousand words in the language. I want completely different rules. Not a translation of these rules. Completely different rules, starting from a completely different axiom. One of the words—let’s say this will be the axiom, I don’t care, for example. And now with a completely different set of rules I will create exactly those same ten thousand words, and all the others will not be legal. Is such a thing possible? In principle yes, right? There’s no reason it shouldn’t be. I can generate a set of rules; I can even prove that there is such a set of rules, one that is completely different, not a translation of this set, but that gives exactly the same collection of legal words in the language.

I call the correspondence Hofstadter made a local correspondence. What does that mean? Every typographical rule can be translated into an arithmetic rule. Therefore I don’t need to go through all the words generated in these two rule systems; I can show—I can prove—that it’s exactly the same set of words, right? Because there is a one-to-one correspondence between the rules. But now I’m proposing to you a completely different set of rules, something entirely different. A word ending in I—you can add two U’s and remove M. It doesn’t matter, something else. It turns out, surprisingly, that this gives exactly the same ten thousand words and excludes all the other words. Exactly the same thing, but a completely different set of rules. This is not a translation of those rules. There is no connection between these rules and those rules, except that they both give the same set of legitimate words in the language. Exactly the same thing.

So now the grammar of the language—if I had given you only the set of words, not the rules of grammar—you could say that the grammar is this and you could say that the grammar is that, right? There’s no way to know which is the correct grammar. But this is what I call a global correspondence, not a local correspondence. I cannot show, prove, that the words are identical in these two systems of rules, because there is no connection between those systems of rules. At most, what I can do is generate the whole dictionary with this, generate the whole dictionary with that, and see whether there is identity between the dictionaries de facto. But I cannot prove in advance that the two dictionaries will be identical, because there is no connection between the rule systems. That is the property of a global system.

Now think about a global system that gives you the same ten thousand words except for one. If the correspondence is a local correspondence, that can’t happen, right? If for each of the three typographical rules I translate it into a rule completely equivalent to it on the arithmetic plane, then of course the dictionary will be completely identical. It’s simply mathematical. Everything you produce with this you produce with that; it’s entirely equivalent, right? That’s obvious. But when the correspondence is a global correspondence, then there’s no conceptual problem—just as I could produce a set of rules that gives the same ten thousand words even though the rules are completely different, I can produce a set of rules that gives nine thousand nine hundred and ninety-eight words and two others, or doesn’t give two at all. In other words, it will differ from the original dictionary by only two words, or by five words, or it will add three more words. But there will be specific points at which the correspondence between Hofstadter’s rules and the rules I’m proposing is damaged. You understand that if the correspondence is local this is impossible, but if the correspondence is global it is possible. If the correspondence is global, then it may be almost complete but not entirely, because in any case it’s only a coincidence that there is a correspondence, okay?

So what exactly is my claim? My claim is that the relation between the revealed and the hidden is not a local correspondence but a global correspondence—or between the mystical, forget Kabbalah, I’m not talking about Kabbalah specifically; Kabbalah is the example that always accompanies us, but I’m talking about mysticism in general. The claim is that if there is a complete, whole mystical system that provides a complete explanation of the facts it deals with, then the relation between it and the revealed explanation can be one of two things. Either it is simply a translation, and probably a local translation, or there is a global relation between them and then it really is not a translation, it is another explanation—and then it can also be, and is even likely, that there will be points where the correspondence breaks. Because what are the chances that a different rule system will fit this system perfectly even though there is no connection between them? There’s a reasonable chance that there is some correspondence, that you manage to get perhaps a good correspondence, but there will be points where it breaks.

What do I want to say? I want to say: let’s look at Kabbalah or at theology and science. Fine? Suppose that for every event in the world I can offer a scientific explanation and I can offer a theological explanation. But if I want to make a local correspondence, I’m really saying that there is a theological correlate to Newton’s law of gravity. Yes, the kindness within hod attracts the eternity within tiferet with an intensity proportional to—I don’t know—to the ray of creation of the system, I don’t know—translate all of Newton’s words into spoken Kabbalistic language. Okay? So in effect you are saying that this is a translation into a different language. Then of course everything that has a scientific explanation will have a theological explanation and vice versa. The correspondence will be perfect, because it’s just a different language for describing the same thing.

But if I claim that there is a global correspondence, not a local one—what does that mean? The set of theological rules will produce a general pattern of behavior in the world similar to the set of scientific rules. Broadly speaking it will look similar. But there will be places where it doesn’t match. What does that mean? It basically means that theology is not a translation of science. It really is another explanation. Only, surprisingly or not surprisingly—maybe the Holy One, blessed be He, arranged it in advance, it doesn’t matter—but there is a correspondence in the phenomena. In other words, the correspondence is not in the rules; I cannot find a theological correlate to the law of gravity. But the collection of phenomena that the laws of physics generate, the laws of theology also generate. Even though there is no local one-to-one connection of physical law against theological law. It is a completely different set of laws. But the words in the language—yes, in Wittgenstein those are the words in the language; for us they are the events in the world. The events in the world can be explained by the theological system of rules and by the scientific system of rules. And usually it will give the same result even though there is no identification, no translation. These are not two different languages that describe the same thing. This is a global correspondence. And therefore there will be situations in which it breaks. Because there’s no way—like with, say, let’s imagine the Holy One, blessed be He—let’s imagine theology as a Cartesian coordinate system and science as a polar coordinate system. Okay? Then that means that in the polar system there will be something that cannot be described purely in Cartesian terms: the point x equals zero, y equals zero. That is a scriptural decree, right? Or it is a miracle. There is no scientific explanation for it, or no explanation in the revealed realm; there is an explanation in the hidden realm.

What does that mean? It means that it is not correct to look at polar and Cartesian as translations. They are not translations of two different languages describing the same thing. They are two different things. Not translations. There is a correspondence between them, surprisingly or not surprisingly—there is a correspondence in the overwhelming majority of the things being explained, in this case the points on the plane. But there is a point that doesn’t fit, or points that don’t fit. And once there is a point that doesn’t fit, you understand that this cannot merely be one translating the other. They are two different systems. One point where there is no correspondence is enough to show that in fact you cannot find a one-to-one and onto mapping—yes?—between these rules and those rules. Clearly it breaks. If there were such a mapping, then it would have to be entirely identical.

On the other hand, I do want to claim that it is true that we have here two explanations that both claim the crown of being an explanation. Both try to offer a complete explanation of the phenomenon. And in the overwhelming majority of cases this will work. Sometimes not. Yes, it’s like the method of Tosafot, yes? A little less here, a little more there—they raise a difficulty, no no, it’s a little here and a little less there—it’s the kind of thing that makes the hair of an ordinary learned person stand on end when he reads such answers in Tosafot. But yes, sometimes these are householder’s answers. It fits, but not entirely. Sometimes not. The correspondence is good but not complete. It’s not one or zero. There are correspondences that are not bad, but they’re not complete. You know, even a scientific theory doesn’t really manage to explain all the facts. It explains a sufficient volume of facts to convince us that it has substance. But there are always facts that are still difficult, and you have to keep working, working more. It’s not that we throw out the theory—yes, that’s Thomas Kuhn. We don’t throw out a theory every time we discover a fact that doesn’t fit it. We just have to work a bit more, and sometimes we live with facts that don’t fit.

So here too, I think the picture I described earlier—either the explanations are partial explanations that join together to give an overall explanation, or the explanations are complete explanations but then it must be merely a translation from one language to another—that is too dichotomous a picture. What I want to claim is that the relation between mysticism and the revealed, or between Kabbalah and the revealed, is a relation of global correspondence. Say mysticism offers, Kabbalah offers, an explanation for all the verses of the Torah for the sake of discussion, and there is also a revealed explanation for all the verses of the Torah. That does not mean that every term or every word in the Torah can be translated into the language of Kabbalah. Sometimes Kabbalah will explain chapter 10 verse 2 together with chapter 14 verse 15; they will complement each other within some Kabbalistic move where in the revealed layer there is no connection at all between those verses. The revealed layer explains them completely differently. But the revealed layer offers an explanation for all the verses and the hidden layer also offers an explanation for all the verses. But there is no mapping between the explanations. Everything works out according to this and everything works out according to that, but there is no mapping.

Now once the correspondence is global, it also becomes understandable why there are scriptural decrees. Because a global correspondence can also break; there are topological defects. There are situations in which we will not find a revealed explanation; there is only a hidden explanation. That is the greatest testimony that the correspondence is not a local correspondence. Now sometimes there is a translation. Between Abraham and Sarah, matter and form versus kindness and judgment—that’s roughly a translation; even that is a bit of an exaggerated translation, but let’s call it a translation. But it’s partial. There is no local, one-to-one and onto correspondence between the rules of the revealed and the rules of the hidden. The correspondence is not in the grammatical rules that generate the words; the correspondence is in the words. In other words, the set of events that happen in the world can be explained by the hidden and also by the revealed. The words generated by the rules are identical in the two systems of rules; the words are the events. But as for the rules themselves, there is no mapping between them.

And I think this is the more correct model for describing the relation between mysticism and the revealed, between Kabbalah and the revealed: a global correspondence with topological defects, with points where the correspondence breaks. And this is what I actually want to claim: that mysticism really pretends to offer a different explanation of phenomena; it is not a translation of the explanation into another language. It is a different explanation, another one. Okay? And the revealed offers another explanation; these are different explanations. It is not a translation of the same explanation. And therefore the mystical claim—I mentioned earlier whether it is a metaphor or not a metaphor—the mystical claim is not: there are spiritual forces and they stand behind the events that occur here in the world. And physics will explain it by the physical forces that stand behind the events that occur in the world. One master says one thing and another master says another thing, and they do not disagree. This describes the events in the world and that describes the events in the world. It’s a global correspondence, where in certain places it will break, because it cannot do the job hermetically; that is probably impossible. In certain places it breaks.

Okay, that is more or less the picture I wanted to arrive at up to this point. Does anyone want to comment or ask?

[Speaker H] Yishai, so what is a sufficient condition?

[Rabbi Michael Abraham] I’m saying: the Kabbalistic explanation offers, say, a sufficient condition for the occurrence. The scientific explanation also offers a sufficient condition for the occurrence. Usually the Kabbalistic conditions will occur when the conditions of the revealed occur. But it’s not that they’re the same conditions in a different language; it simply happens—there is a correspondence. You know what, maybe next time I’ll bring some amusing example from Raymond Smullyan about correspondences like that. I might mention it next time. But the claim is that the circumstances of the revealed that caused the occurrence, and the circumstances of the hidden, simply probably happened in parallel. But these are still two different sets of circumstances, and therefore sometimes it will happen without that, or vice versa—the correspondence will break. It is not a description in different languages of the same set of circumstances. These are different circumstances. They are descriptions of different things. That is really the claim. And each one of them is a sufficient condition. I really think I still need this addition; I’ll leave it out for now, I’ll explain that addition next time. Another question or comment? Okay, let’s stop here. Goodbye for now. Thank you very much.