Essential Explanations and Examples – Lesson 2

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[Speaker I] for a reason, the way you slaughter, you look for the easiest death possible, and if today we reach the conclusion, say, that stunning an animal is an easier death, then ostensibly

[Rabbi Michael Abraham] Stunning comes before the slaughter. After that you slaughter following the stunning. But stunning is not an alternative form of slaughter.

[Speaker I] But with all the arguments today about

[Rabbi Michael Abraham] No, in principle that’s not possible. We are still commanded in this, and we cannot deviate from it. But here it can be possible or not possible; rather, it has to be. Maimonides says that these commandments have no reasons, and it is impossible to look for reasons for them. “Know that wisdom required it—or, if you wish, say that necessity brought it about—that there be there elements that have no reason; and it is as though it were impossible, according to the law of the Torah, that there not be something of this kind in it. And the forms this necessity takes—I will explain to you—are such as: why was it a lamb and not a ram? The very same question would have arisen had a ram been stated instead of a lamb. If they had said ram instead of lamb, you would also ask: why a ram and not a lamb? For one species must necessarily be chosen. In other words, some one species has to be fixed, so one species was fixed. And likewise, why were there seven lambs and not eight? For they would also ask this if there were eight, or ten, or twenty, since some number is necessarily required. This resembles the nature of possibility, in which one of the possible alternatives must necessarily exist; and it is useless to ask why this possible alternative rather than another of the possibilities, for this very question would arise if the other possible alternative were found in its place. And this is enough on the matter for one who understands it,” and so on. “As for those who said in all innocence that every commandment has a reason”—you can see this is really right around our topic. In other words, he basically understands the motivation of those who look for reasons. Their motivation is exactly what I’ve been talking about all along: they think that the Holy One, blessed be He, does not do things without a reason. There aren’t things that you do arbitrarily, by lottery, when you could just as well have done the opposite. That would detract from the perfection of the Holy One, blessed be He. Therefore they reach the conclusion—the opponents of Maimonides—that every detail must have a reason. And here Maimonides attacks that point head-on. Maimonides says: that’s not true. There can be a situation in which there is a field of possibilities, different options, and the Holy One, blessed be He, chooses one of them by lot, arbitrarily. We have to do it because the Holy One, blessed be He, commanded us to do it, but it is arbitrary. Of course, he assumes here—and that’s an assumption that needs discussion, but that is what he assumes—what you asked earlier, Tzvika: the assumption is that there still has to be uniformity for some reason. In other words, according to Maimonides’ conception, what the Holy One, blessed be He, should have commanded is exactly what Tzvi said earlier: command us to slaughter; how to slaughter, do whatever you want, what difference does it make? So that, at any rate, is not the case. It does matter whether it’s from the neck or from the nape.

[Speaker C] Why are there lots of details that weren’t fixed? There are roughly infinitely many details in the commandments that weren’t fixed. Okay. Why specifically this… In other words, according to his approach, something has to be fixed—no. He says something has to be fixed because in the end one thing has to be fixed. There are infinitely many things that aren’t like that.

[Rabbi Michael Abraham] Apparently there is some certain level of uniformity that has to exist. Obviously you can’t carry it all the way through so that everyone does exactly the same thing. But there is some certain level. Again, I’m looking at this only from the angle of degrees of freedom. I’m not dealing right now with the issue of reasons for the commandments itself. But in the issue of degrees of freedom, you can see this in Maimonides. Again, this is a classic example, and here he already puts the issue on the table. He says: this is the problem. The theological problem that really drives people not to think this way is precisely the assumption that it is impossible that the Holy One, blessed be He, does things just like that, by lottery, arbitrarily; rather, every single thing has to have some good reason. And Maimonides says: not true. Third example—Maimonides says here as well: not true. There are situations in which the Holy One, blessed be He, does indeed cast lots; He decides something arbitrarily even though He has no reason, because He has to decide something. And again, he has some assumption that there has to be uniformity—that is, it can’t be left open.

[Speaker J] So you can’t say that the commandment itself is arbitrary? Only because Maimonides found a rationale for it? What? If someone found rationality דווקא in the details and not in the commandment itself, then couldn’t it be the other way around?

[Rabbi Michael Abraham] Good point. If this whole business had no reasons at all, that’s impossible.

[Speaker J] Absolutely, but

[Rabbi Michael Abraham] So where do you still draw the line? No, I’m saying: Maimonides apparently assumes that there has to be uniformity. And that assumption needs explanation, but that is his assumption. Now once that assumption exists, everything opens up, because the commandments certainly need a reason. The Holy One, blessed be He, doesn’t do things without a reason. The commandments have a reason; He commands them—it’s not the same as peacocks. Right, we talked about peacocks. Here He is commanding us something; apparently He wants to achieve something. Otherwise it’s just unreasonable. Maimonides himself says that those who think the Holy One, blessed be He, gives commandments without reasons make the Holy One, blessed be He, inferior to His creatures—His creatures do things only if they have logic to them, while the Holy One, blessed be He, does things without logic. In other words, that’s not unreasonable. So things need a reason. But what? Obviously the reasons reach only the principle of the commandment. Now within the details of the commandment—

[Speaker J] Maybe some of the details also join that logic, but not all of them. Some of the details need to be fixed arbitrarily; then you ask why fix them at all. But I think maybe you can explain it the same way—just transfer it. Now, from among all the possible details, let’s choose the details that have the most logic in them. So why a lamb and not a ram? Because with a lamb it will be most similar to a lot of things. I agree, I’m just asking why you can’t carry that logic all the way through.

[Rabbi Michael Abraham] That’s exactly the approach he’s arguing against. There is such an approach.

[Speaker C] Maybe because he sees that there aren’t—he says there are no reasons here.

[Rabbi Michael Abraham] He says more than that—he says something stronger. Not only that he sees it. He says it can’t be otherwise. Exactly—that’s the problem. The point is, obviously you can achieve the goal in several ways. It’s impossible that there not be some degree of freedom in which you do end up making a lottery. In other words, there’s a stronger claim here than simply: look, I see, it doesn’t seem to me that there’s a reason here, so I have no choice, so I say okay, apparently this is without a reason. It seems he even attacks those who look for reasons in the first place. Why on earth? I mean, if you are running such a large, complex, sprawling system, there will undoubtedly be degrees of freedom in it that you will not be able to determine in light of the basic rationale of the commandment. You want to slaughter a certain animal—there is some reason for that. Now from that reason you won’t manage to derive all the details of the laws of slaughter. On the other hand—again, this is the assumption Maimonides introduces here, and it requires explanation, but he does introduce it—there has to be uniformity. In other words, Jewish law does have to determine what to do with the details as well. He is not willing to accept the possibility that it remain open. And then he says: if so, then there has to be some degree of freedom here. In that sense, this example joins the previous two examples, where Maimonides basically does accept, on the theological level—and here, where he really puts it on the table, this problem—here he explicitly states his theological position independent of reasons for the commandments. The Holy One, blessed be He, can make lotteries. There is no theological contradiction in the claim that the Holy One, blessed be He, can make lotteries. That’s really the point. And therefore, if I return to Israel’s special quality, Maimonides’ conception of Israel’s special quality is also not like the Kuzari. In other words, there too he sees it as a kind of lottery. The Holy One, blessed be He, chose us, and as a result we became the chosen people. Meaning, He could also have chosen a different nation.

[Speaker C] But then if He chose us on the basis of His intellect, how can He make a lottery? What? How theoretically can He make a lottery? For us, maybe we can make a lottery by disconnecting choice, kind of by not choosing, and then our nature is built in a certain way so that something happens—like if I spin, I don’t know. So maybe it’s just some kind of structure. We have a certain structure.

[Rabbi Michael Abraham] Or a lottery—rolling a die isn’t really a lottery.

[Speaker C] All those things aren’t really a lottery.

[Rabbi Michael Abraham] No, of course. Rolling a die is not an option for the Holy One, blessed be He, to use as a lottery. Even if I say He just presses something at random. A quantum jump. Even if I say He just presses something at random—quanta. That’s a real lottery, and the Holy One, blessed be He, can do that too.

[Speaker C] Any lottery that isn’t real—

[Rabbi Michael Abraham] Like dice—you’re right—the Holy One, blessed be He, knows what will come out. He knows Newton’s laws, He’ll do the calculation, He knows it will fall on five. He can’t make a lottery that way. So He can make a quantum lottery, a real one, where there is genuine randomness. And genuine randomness He also cannot control. It could be—but then it wouldn’t be random.

[Speaker D] Right, but then He would know what the result will be.

[Rabbi Michael Abraham] No, He would not know. If it’s randomness—genuine randomness—then He does not know. That’s the point. Anyway, we’re returning to earlier arguments here.

[Speaker D] It explicitly says, “a disgraceful and unwise people,” and later it says, “Is He not your Father, your Master? He made you and established you.” He builds us; through the commandments He builds us. It’s not that we’re more special than everyone else—“a disgraceful and unwise people.”

[Rabbi Michael Abraham] Okay, I don’t know.

[Speaker D] “Is He not your Father, your Master?” He educates us every day through the commandments. Apparently there is something here: it’s the education that makes us.

[Rabbi Michael Abraham] Fine, I completely agree with that conception, but you know, there are many who do not agree. In any case, in these three examples we see the conception that Maimonides very clearly does accept the possibility of degrees of freedom. Now here I want to go back—this relates to all the examples, but it especially relates to the second example, of providence over the species. Here I also come to Shmuel’s remark earlier, which I said I’d get back to. Providence over the species is really an interesting phenomenon, because there is here—actually it reminds me of something else; maybe I’ll get to it in this context. We once spoke about Leibniz’s principle, the identity of indiscernibles. I think I talked about it. Leibniz claims that if there are two bodies that have the same set of characteristics, then it is one body, not two. In other words, if there are two, then there has to be something different in one as against the other, some property in one that differs from the other. Now again, if we include place as well—place seems to people like a trivial principle, if we include place as a property too. In other words, if they have the same place too and the same—well then it really is the same entity. But that’s not exact. There can be two entities that are completely identical and also in the same place. The fact that two entities cannot be in the same place is just a physical fact; it is not a logical contradiction. If there are photons or things like that, where there is no rigid body between them—yes, there is no repulsive force between them—they don’t occupy space. Yes, they don’t occupy space; there is no mutual repulsive force between them, so they can also be in the same place. There is nothing sacred about place that individuates entities. So that claim is not only non-trivial; I also think it’s false. Not only is it non-trivial—I’m convinced it’s false. In other words, I think he is mistaken. It is definitely possible for different entities to have the same set of properties.

[Speaker B] And we talked about this—in what sense are they different?

[Rabbi Michael Abraham] Right, so I said, I discussed it. Leibniz’s proof was by contradiction. Let us assume there are two entities with the same set of properties and they are still two, and let’s see that this leads to a contradiction. Entity A has the property that it is not B, and entity B does not have that property. So therefore they do not have the same set of properties. So we have refuted the assumption, right? The assumption led to a contradiction with itself, and therefore the assumption is incorrect. It is impossible that there be two different entities here that have the same set of properties. Now this is like every—I gave this in the context, I think I gave it in the context when we talked about, in the year we dealt with logic. I said that every logical argument begs the question, and I gave this as an example of a logical argument that begs the question. This proof is not correct. Even though it looks terribly persuasive, it is not correct.

[Speaker D] And if I had one body and cut it in two? If I had—if I had one lump of plasticine, one lump of plasticine, and I cut it in two.

[Rabbi Michael Abraham] Now you have two different bodies, each of which is half a lump of plasticine.

[Speaker D] Why are they separate? Because they’re next to each other?

[Rabbi Michael Abraham] Yes, because they’re in a different place, for example, yes.

[Speaker D] If I divide space, divide that stretch of desert and suddenly—

[Rabbi Michael Abraham] There was some tremor, fine, so now the place has become two places. What difference does it make? So now there are two because there are two—two places. They are also different. Why not? Place is a property. Why not? Being in a certain place is also a kind of property. A body can have it. Fine, doesn’t matter—there can be all kinds of properties; that too is a property. I’m saying: why is his proof not a proof? And as a general rule, keep this firmly in your hand: no proof can bring you to something you don’t agree with. In other words, if you don’t agree with the conclusion, look for where it is in the premises. In other words, whoever brings you a claim, a logical proof—there is no logical proof that doesn’t suffer from this issue. There isn’t; it cannot be otherwise, because otherwise it wouldn’t be a valid argument. So what’s happening here? The claim that stands against Leibniz’s conception is that the otherness of a body is not a property. In other words, its being different from the other body is not one of the set of properties. That is not a property. When I speak about the properties of a thing, I’m speaking about what characterizes it: that it’s brown, kindhearted, tall, square, whatever—various properties of that sort. Yellow, that’s it, located here. But existing—for example, that it exists—that is some sort of statement that is not a property of the thing. The thing exists—that’s not a statement that it has a property, namely existence. If it weren’t here, it wouldn’t be. That’s not a property of someone who existed with or without that property. Therefore, to say of the thing that it exists is not to refer to one of its properties, its form—what I called its essence, its being. Okay. Now the claim against Leibniz basically says: there are two bodies that have exactly the same set of properties and they are still two. Why are they two? Because there is something in a body beyond the totality of its properties, and that is the body itself, the bearer of the properties. The body that bears the properties is something additional; the body is not just a bundle of properties. Leibniz assumes that a body is a bundle of properties, and then he says that once the bundle of properties is identical, come on, it’s the same body. But someone who stands against him—right now I’m not getting into whether he’s right or not—but what is the counterclaim? The counterclaim says there is something in the body beyond the totality of its properties. And to my mind that is a trivial claim. Of course—there is the body itself, the bearer of the properties, that which is characterized by those properties. Now once there is something in the body besides the totality of the properties, what problem is there in thinking that there are two somethings carrying the same set of properties on their backs, and they are still two? And now if you go back over Leibniz’s proof, you’ll see it doesn’t hold water, because to say that A is not B is not a property of A. Exactly. Therefore every proof begs the question. Always. Sometimes it’s hidden; sometimes it’s tricky. There’s no way around it—no proof can fail to beg the question. No tricks; there are no exceptions here. A valid argument always begs the question. Therefore never believe valid arguments. It’s a bit the opposite of reason. Valid arguments seem like the most persuasive tool. A valid argument is the least persuasive thing there is, because it always begs the question.

[Speaker B] No, you can—if you agree on the premises—

[Rabbi Michael Abraham] Yes, sometimes a valid argument really reveals some basic mistake you made. If you agree to the premises and suddenly discover that the conclusion is not—

[Speaker B] If you assume—you agree to the premises of Euclidean geometry—

[Rabbi Michael Abraham] Yes, yes, of course. Three premises. Then believe that in a triangle there are—

[Speaker B] one hundred and eighty, but—

[Rabbi Michael Abraham] Then they’ve just uncovered a mistake on your part. But then they’ve only uncovered a simple conceptual mistake on your part. Usually that’s not the situation. No, the discovery can be experiential, I understand, but you thought there were two hundred and thirty degrees in a triangle. Ah, you simply didn’t know—that’s not what I mean. I’m talking about an argument, a dispute in which someone argues against you and raises a valid argument. If he raises a valid argument, then it can happen that you simply missed something in the logical calculation—that is, you agree with the premises but did not arrive at the conclusion.

[Speaker B] If there’s a dispute about a valid argument, then the dispute is always about the premises and not about the conclusion.

[Rabbi Michael Abraham] Exactly—that’s the claim. Therefore, once you don’t agree with the conclusion, look for where in the premises you disagree.

[Speaker D] That’s the point. Properties are always predicates, it seems to me.

[Rabbi Michael Abraham] Huh? Yes, correct. Properties are predicates.

[Speaker D] Like Maimonides said. Yes, yes, I spoke about this. It’s always a predicate, and the body itself is not a predicate.

[Rabbi Michael Abraham] Correct. So that’s exactly what I spoke about in this context—about predicates. Now, for our purposes—ah, one of the examples that came to mind when I thought about this Leibniz issue: in physics they divide between two kinds of particles. There are bosons and fermions. Fermions are particles of a kind that cannot be found characterized by the same set of properties. There are no two particles characterized by the same set of properties. If there are two particles, that means that something in their properties differs. They are Leibnizian particles, so to speak. But there are other particles called bosons—after the Indian physicist Bose, yes. So there are particles called bosons, which are not fermions—that is, they can be found in exactly the same—what is called the same state, yes. They have exactly the same physical properties, and a Bose-Einstein condensate, that’s what it’s called—in other words, never mind—it’s a collection of particles that collapse into a state in which they all occupy the lowest state, not important on what scale, and they have exactly the same properties. And all the particles—we have a number; we know how many particles are there. According to Leibniz, such a thing is impossible. Because if all of them have exactly the same physical properties, then by definition there is one particle there. Now of course—wait, does that include location?

[Speaker K] By another name.

[Rabbi Michael Abraham] He would call it one large particle whose property is n times the small property.

[Speaker K] Ah, or he would say there are seven particles here, and the property distinguishing them is that A is not B, B is not C, C is not D, and so on.

[Rabbi Michael Abraham] So that’s the same thing. Exactly, that’s the same thing. So what do you mean? If so, then he said nothing. So Leibniz said nothing. Of course there are no two different particles for which it is not true that A is not B. In other words, obviously A is not B if it is different. That’s just a translation. Huh? Fine—if he said nothing, then I’m not arguing with him, I have no problem. But the principle of charity says that if someone says something, we interpret it in a way that… And with Leibniz you really don’t need a great deal of charity to interpret him; he was a wise man. In any event, bosons are a good example of this issue, because there we see a totality and we count how many particles there are, even though all the particles have exactly the same physical properties—that’s the definition. Also location? Everything—location, everything is the same. Location too, yes. Everything is the same. Location, velocity—they’re not… So how do you distinguish them? So what is it? They’re not little balls; it’s something else.

[Speaker C] So how do you count them?

[Rabbi Michael Abraham] You don’t count them by raising hands. There are, by the way, crazy tricks with bosons in the statistical mechanics of bosons. For example, you can swap two bosons and nothing will happen. But you count numbers—it still shows up in the number of states, that there is some number of bosons. In other words, the entropy shows that there are n particles here, because the question is in how many arrangements you can do it, even though they are identical particles. Okay? So there are physical manifestations of the fact—

[Speaker C] that you don’t arrange them in that place.

[Rabbi Michael Abraham] Exactly. Not arranging them. Exactly, that’s what I’m saying. It’s not arranging—meaning, that’s exactly the point. You can swap all of them with all of them because it has no significance whatsoever; they are all in the same state. That’s exactly the point.

[Speaker C] Can you take one out?

[Rabbi Michael Abraham] You can—it’s just not accessible to tweezers. You don’t—no, no, not even to abstract tweezers. In other words, you can’t take one and remove it.

[Speaker C] I don’t know, in some way, kill one, to—

[Rabbi Michael Abraham] You see now how this connects to peacocks. You can’t say that particle seventeen disappeared. One out of a hundred particles disappeared. Now we have ninety-nine. You have no idea—not only do you have no idea, there is no numbering. Yes. You can’t number the particles; they don’t have an identity that is preserved. Exactly. They have no identity preserved over time. Now these things create paradoxes—Gibbs’ paradox, for those who know thermodynamics, comes from these things. The fact that you do not have an identity preserved over time for the particle—it loses its identity because it has none; you cannot distinguish it from anything else. You can swap particles there, and that creates entropies and all sorts of things; all kinds of things come out of nowhere because of these problems. But the fact is that there are n particles; there are indicators of this. Now I use exactly this to return to the discussion of the degrees of freedom of the peacocks. Because suppose the Holy One, blessed be He, wants there to be such a condensate with a hundred bosons. A heap of a hundred bosons. Because it does something in the world; I don’t know exactly what. It can’t be achieved in any other way, at least given the laws we know. Okay, you need a hundred bosons. But it doesn’t matter one bit whether boson seventeen—which doesn’t really exist as such—is swapped with boson ninety-four. Not only does it not matter, the words ‘swap them with each other’ have no meaning. Would such a thing be called providence over the collective or providence over the individual? I don’t know what to say. Because I don’t know whether it is really correct—now I return to Ari’s remark earlier—whether it is really correct to speak here about a hundred particles, or whether that’s just a manner of speaking. In truth there is some sort of whole here, one creature. Not several creatures—one creature. We call it a hundred bosons in the same state. What difference does it make? But it is one creature that has certain properties, and that’s all. Why assume there are a hundred creatures all mixed together?

[Speaker C] Why assume it? That’s reality.

[Rabbi Michael Abraham] What does ‘reality’ mean? In what sense is that reality?

[Speaker C] That’s what we tried and didn’t fully understand.

[Rabbi Michael Abraham] No, that’s what I’m saying. In physics they always see it that way; to physicists it seems terribly obvious. Someone seeing it from outside really says: wait, so why treat it as a hundred things at all? Let’s see it as one thing. We call it a hundred particles, but that’s nonsense—what difference does it make? It’s just words.

[Speaker C] But that’s through a physicist’s eyes.

[Rabbi Michael Abraham] We are looking at it through eyes—no, the opposite, in my eyes—

[Speaker C] not through a physicist’s eyes, through healthy eyes. The physicist here, in that sense, is captive.

[Rabbi Michael Abraham] But sometimes the outside view is more correct. So if I look at such a collection of particles, I’m not at all sure there is any meaning to speaking about providence over the individual as opposed to providence over the whole. Providence over the whole is providence over the individuals, because the individuals have no ID cards at all; there really are no individuals here. It’s like—not exactly like, but perhaps a distant analogy—also a person is a kind of collective, right? He has a collection of molecules. And to all of us it is fairly intuitively clear that the human being as a whole is still some kind of creature with significance in itself; it is not merely the collection of molecules. If the collection of molecules were all concentrated in a big pot, we would not call that a human being, right? A human being is something that is not just the collection of molecules composing him. Now when I need there to be a human being in the world, a human being is built from molecules—there is no other way to build him. Now whether you take this molecule or that molecule, it changes nothing, because what I need here is a human being. So here it is not like bosons, because here the molecules do in principle have identity. You can swap any molecule, remove it, put another in its place. A molecule is a large body, so it has an identity card. But on the conceptual level—and here I return to Maimonides—I see no obstacle to saying that the Holy One, blessed be He, wanted a human being. This human being needs I don’t know how many molecules in order for his body to function the way the Holy One, blessed be He, wants it to function. So why does the Holy One, blessed be He, need to supervise every molecule in order to be perfect? A human being needs to be composed of such-and-such a number of molecules, so He needs that number of molecules. Why should I care if those molecules can be swapped one with another and nothing changes? Fair enough—nothing changes. So what? But it still remains the case that the Holy One, blessed be He, needs a heap of molecules in a certain number, in a certain structure, that will create a human being. That He needs. I think what I’m trying to say is that there really is something precise here in a certain sense. The theological claim was that the Holy One, blessed be He, is doing something arbitrary, not precise—there is a degree of freedom here. There is no degree of freedom, because you need a hundred million molecules to produce a human being. I’m just making up a number—one hundred million molecules to produce a human being. That you need in any case. Now what—you also have to find a role for each molecule? You want a human being—that’s what you want, you don’t want molecules. Does that mean there is some deficiency here in the omnipotence, in the perfection, of the Holy One, blessed be He? He needs a creature with a hundred million molecules, just as He needs that Bose-Einstein thing. If He needs a condensate of a hundred bosons, then He needs that creature of a hundred bosons. It is true that with bosons there are no identity cards, and in that sense it is not at all clear that we are talking about a hundred creatures; rather, we are talking about one collective creature, that’s all. But with fermions—or with molecules and a human being—the idea can certainly remain. There is no problem whatsoever with the statement, “I need this heap to function for me like a human being.” I don’t care if the seventeenth molecule from the right is swapped with molecule ninety-five on the left. What difference does it make?

[Speaker C] According to chaos theory, doesn’t it actually matter? I mean, the same thing or the same molecule—every little thing, there’s here—

[Rabbi Michael Abraham] No, but this isn’t a chaotic thing. They’re identical, identical. Let’s assume for the moment that they’re identical.

[Speaker C] It doesn’t matter how they got from here to there, doesn’t matter.

[Rabbi Michael Abraham] Not everything is chaotic. Chaos is chaos, very nice, but not everything is chaotic. Not every system is chaotic. There are certain systems in which there is chaos. The butterfly—people think every little thing must immediately cause… It’s not like that. There are certain systems in nature that have a chaotic character.

[Speaker C] It doesn’t have to cause an avalanche, it doesn’t have to cause something big. Even if it causes something small, I mean a small change will cause a chain of small changes. What?

[Rabbi Michael Abraham] For that you don’t need chaos. Just say: so does He care about the small change?

[Speaker C] No, but in the end—

[Rabbi Michael Abraham] In the end it will lead to a change—no, it won’t; in chaos, in the end it always… No, it won’t. He wants the small change. It doesn’t have to lead to a big change. So I’m saying: let us assume they are identical, the molecules, for the sake of the discussion. You need a hundred million identical molecules.

[Speaker C] It doesn’t matter—even if they’re identical, they have a path by which they got where they got. The motion that caused them to get there also includes things such that if the motion had been different, then it would have caused—

[Rabbi Michael Abraham] No problem. Then another molecule would have arrived here and another molecule there, and I would look the same.

[Speaker C] Given the constraints of a complex world, maybe that’s the only way to do it, or I don’t know, almost the only way.

[Rabbi Michael Abraham] I’m saying, it’s the same as the explanations you suggested for what Maimonides said earlier. I’m willing to accept that. I’m only saying that I don’t see why—why say that? There is no obstacle. It is also a completely defined will when the Holy One, blessed be He, wants a creature composed of a hundred million molecules. Why does it detract in any way from His perfection if you can swap the positions of the molecules? Optimization? But that isn’t optimization, because I need a hundred million molecules. Why does each one need a role?

[Speaker C] Optimization would be the minimum complexity of something to achieve the result, right? You want—

[Rabbi Michael Abraham] That is the minimum. With less than that there is no human being.

[Speaker C] Why can’t it be done in a way that won’t have several options but only one way, the most complex one?

[Rabbi Michael Abraham] No, but then there would be no human being. A human being is composed in this way. I want this kind of human being because he fulfills what I want from human beings.

[Speaker C] Fine? So why then could you create a creature more perfect than a human being?

[Rabbi Michael Abraham] I can’t. There is no better creature. This is the optimum, the best that fulfills what I want from it.

[Speaker C] So maybe that’s the question: you created a system that seems a bit inefficient.

[Rabbi Michael Abraham] So that’s what I’m saying—no, I don’t think it’s inefficient. That’s exactly the point. Where my requirement is a requirement on the collective, that’s what I want. I want there to be a thousand peacocks in the world because it is important, I don’t know, for the ecology of the world. So I want a thousand peacocks. I’m not interested in what peacock seventeen and peacock nine hundred do. It doesn’t matter. But I need a thousand peacocks. So what’s the problem? I made a heap of a thousand peacocks here, that’s all. Now from my standpoint, regard all these thousand peacocks as one creature, as though they were bosons, okay? One creature with no identity card. This creature of the thousand peacocks—the heap of a thousand peacocks—has a defined role, and it is under providence, and everything is the same as with human beings. That’s all. It’s just a collective creature. That’s it. And over this collective creature the Holy One, blessed be He, exercises providence, and everything is fine, and He wants everything to proceed as He wants. That’s all—but over the collective creature, not over the individuals. In statistical mechanics, actually, the examples I gave earlier are related to it. Statistical mechanics in general has two… The great innovation of statistical mechanics—when they started the statistical mechanics course, I studied it at Tel Aviv University, I’ll never forget it as long as I live—was for me like the giving of the Torah. Truly the giving of the Torah. It’s unbelievable. I mean, you study laws of thermodynamics—laws about how heat and energy and all kinds of things like that behave, and entropy, all kinds of quantities that mean nothing to you, it’s hard to understand what those quantities are even saying. Then on the board there appears the simplest possible model of a few particles that have velocity and position and so on. All in all, you simply define certain properties—you say, for example, what the total energy of the system is; you say the energy of each particle summed over all the particles, that is the total energy of the system. And then you begin defining quantities on this particle system, and suddenly by something like a miracle you get all the laws of thermodynamics. Out of statistical mechanics. Statistical mechanics is basically a microscopic model that yields all the laws of thermodynamics from almost zero assumptions and perfectly self-evident ones. It’s simply one of the greatest miracles I’ve ever seen. It was really so illuminating—it was an intellectual experience without equal to learn that. I recommend it to anyone who gets the chance, really. It’s amazing. And the whole idea of it was that you now take, say, let’s talk about a gas—a gas of particles. Today this is a lot of physics, but I think these are the most basic ideas of statistical mechanics, as we are discussing here. You take a gas of particles and you say: look, there is a collection of particles moving inside a box. Each one has some location and some velocity, fine—that’s it, that’s what you have. From this you can derive all the properties of an ideal gas, all the entropy, energy, temperature, whatever you want, from viewing an ideal gas as a collection of classical particles, each of which has velocity, position, energy, momentum, and all the things you define for a particle—

[Speaker B] an individual one, pressure, yes—

[Rabbi Michael Abraham] pressure—all the properties of a gas you can derive from that. Now what happens? When I look at the totality of the particles, I speak in a completely different language from the language in which I speak on the level of the individual particle. At the level of the individual particle, I speak about the velocity of a particle—

[Speaker B] there’s no temperature, no pressure—

[Rabbi Michael Abraham] Yes, exactly. There’s no meaning to talking about the temperature of a single particle; there’s no such thing. Temperature is a property only of a state where you have a large collection of particles. Okay? It doesn’t exist at the level of a single particle. Another example I once gave, I think from John Searle, is about the relationship between body and soul. He wanted to argue that the soul is really the bodily whole. Meaning, there is no additional substance besides matter; the totality of the body is what we call the soul. That was his claim. And he wanted to give an example of this. By the way, today this is very common—emergence? Yes, that’s emergence. Back then the term didn’t yet exist; he was one of the first to formulate it, and today it’s very popular. And the example he gave for this was a property, the property of liquidity. When we look at the property of liquidity—say we take water—water has a property: it is liquid at room temperature, okay? Every single molecule of water is not liquid. It’s not—there is no state of aggregation for it. A single molecule has no state of aggregation. States of aggregation are states of a collection of molecules. It is not gas, not solid, and not liquid. A single molecule is a single molecule; it is the same thing in all states of aggregation. But the collection of molecules can be liquid, solid, or gas. So he says that liquidity is a property that characterizes the collection of molecules, but it does not exist at all in the language of the single molecule. It simply doesn’t exist in that language.

Now when I want to create a liquid—now let’s go back to the Holy One, blessed be He—when I want to create a liquid, fine, then clearly the molecules have all sorts of properties in the language of the single molecule, but I only care that there be a liquid; I don’t care what happens in the molecule. But in order for there to be a liquid, I need a collection of molecules with various properties; there is no other way to do it. In that sense there is no degree of freedom here. There are degrees of freedom in the microscopic sense: you can take molecule number three—assuming they have ID cards at the moment—take molecule three and swap it with molecule five, and nothing will happen, because they’re the same thing. The macroscopic properties of the liquid will look the same; it will remain liquid, its temperature will be the same temperature, its energy will be the same energy, it won’t feel at all that you swapped two elements inside it. Right? So that’s a degree of freedom in the microscopic sense, but in the macroscopic sense you didn’t do anything.

Basically, in statistical mechanics we take a collection of very many microscopic states, all of which have the same set of macroscopic properties. Meaning, you can switch roles among various particles and that won’t change anything at the macro level, because after all, what difference does it make to the total energy if particle number two trades places with particle number five? As long as this one’s energy moved to that one and that one’s energy moved to this one, the sum of all the energies stays the same. It changes nothing. Why should I care whether particle two is here or particle five is here? It’s not important at all, right? Or the density of a gas in a container. If the density is such-and-such per cubic centimeter—so many particles per cubic centimeter—switch particles between places and it won’t change the density of the gas, right. Meaning, properties—the basic idea in statistical mechanics is that we relate to large systems on two levels. On one level we speak about the individual particles, and that’s a whole language of individual particles; that’s the basic mechanics that people study, the mechanics of individual point bodies. Fine? Then there’s the macro language. In the macro language it’s an entirely different language. There is no velocity there, no momentum. There is no position; those concepts do not appear there. Not just that they aren’t used—they are irrelevant to the macroscopic body. For the macroscopic body you speak in concepts like entropy, temperature, energy, pressure, liquidity, state of aggregation, and so on. Okay? It’s a completely different language. But we are talking about the same thing.

Leibowitz once said: try to describe the action of a computer by a precise description. Give me the data on every electron inside this computer—what its velocity and position are at every given moment. Fine? That gives complete information about the computer. Complete information about the computer. Yes, everything else is static; the electrons move. The electrons—give me position and velocity. Position and velocity are already a problem in quantum mechanics, but never mind. Give me position and velocity at every point in time for every electron. Once you’ve described that to me, you’ve described the computer fully.

Now think that you have all that data. Do you have any idea what this computer is doing? Is it now performing the operation one plus one equals two? You will never know that. Never. How could you ever extract from the positions of electrons—think about how many billions upon billions upon billions of electrons, each one with a position and velocity—that’s it, that’s the whole computer, there’s nothing in it except the computer user. Yes.

[Speaker C] Yes.

[Rabbi Michael Abraham] No, even using the computer won’t help you, because you don’t even know what to look for. And even if I did know what to look for, I still wouldn’t find it, never. It’s not a question of computational power at all. You don’t know what to look for. If you don’t understand—I’ll give you an example—if you don’t understand that electrons hitting the screen and creating this symbol and then this symbol and then this symbol and this one, and after that this symbol—one plus one equals two, right?—basically tell you that the computer has now performed the operation one plus one equals two—the computer did not perform the operation one plus one equals two. The computer works with electromagnetic fields and moves electrons. That’s all. Your interpretation, because that’s how you built it, is that what happened here is an addition operation. No computer will discover that.

[Speaker C] It could do that for any operation though. It could collect all that data, just like you do.

[Rabbi Michael Abraham] But it will never be able to know that this is about one plus one and that the result is two.

[Speaker J] But that could be true of any action in the world, not just a computer.

[Rabbi Michael Abraham] It’s fixed, everything—

[Speaker J] Fixed, and even elementary, so to speak.

[Rabbi Michael Abraham] But with respect to a specific computer, where you know its structure—

[Speaker D] You see a picture of the word, of the number two; it doesn’t know what it’s doing.

[Rabbi Michael Abraham] What you see there is electrons flying around. Someone who doesn’t write one and one and plus the way we do will never be able to decipher what the computer is doing. It will look to him like some kind of insane phenomenon.

[Speaker C] Isn’t this a computer programmed by a person who knows what one plus one is?

[Speaker J] Exactly, that’s what he did.

[Rabbi Michael Abraham] That’s exactly the point.

[Speaker C] So that’s true for every action, right? If there’s someone who restores all that information—

[Rabbi Michael Abraham] Then it’s not just the computer; it’s the computer including the person who built it. Right. Fine. But if that’s true for every action—well, that’s no great insight, so why do you need the computer? Just look yourself and see; you can do it on your own even without a computer.

[Speaker C] No, because on your own you won’t manage to see it, but if you’re able to connect all the information—

[Rabbi Michael Abraham] If you know where the screen is and everything else, and you know which electrons to look at, maybe you could do it too, no problem. So yes, certainly. What I’m saying is: again, this is looking at the same thing on two levels. You can look at it on the physical level, and then it is a collection of electrons, electromagnetic fields—incredibly complicated, of course—but fine, on the conceptual level, a very, very powerful computer, an infinite one, could handle that problem. It would give you the position and velocity of every electron at every point in time. And it would help you in no way whatsoever. With all the greatest computational power imaginable, it would help you in no way at all, because you don’t understand the meaning of the data. You don’t know what to look for; you don’t understand the laws of the macro level. The language of the micro and the language of the macro do not talk to each other. They are two completely independent languages.

In a computer, even more than just micro and macro, there are several different language levels. You can talk at the level of gates, you can talk at the level of an individual transistor, you can talk at the level of logic gates—yes, even beyond that—you can talk at the level of software altogether; there are many levels of integration. And in all of them there is compilation—micro, assembly, and so on, exactly.

[Speaker J] That compilation is basically what you’re doing.

[Rabbi Michael Abraham] Exactly, right. And without that, nothing helps. So physics does not give you that answer. Therefore the macroscopic language cannot be built out of the microscopic language unless I already know in advance what I’m looking for. And in statistical mechanics, that was the great genius. They built the microscopic language in such a way that one could define from it the macroscopic language and give it meaning. But they built it that way, because otherwise you couldn’t extract it from the microscopic language.

Now, in statistical mechanics this is everybody’s daily bread. That’s what people do there all the time. You say: in the microscopic language you are inside a jumble of data that tells you nothing. But it’s also not interesting. Who cares what the position and velocity of every particle are at every point in time? Who cares? What interests me is: what is the pressure of this gas, what volume does it occupy, what is its temperature, how much energy does it have? Those are all macroscopic properties of the gas. Now if I know those, why should I care what’s happening with each individual particle?

So in that sense this is a very good analogy to the providence Maimonides speaks about as providence over the species. When I want a liquid at a certain temperature—the Creator of the world, when He wants a liquid at a certain temperature, with such-and-such energy, with such-and-such pressure, in a given volume—that’s it. Now how to build the microscopic structure that will produce those macroscopic properties? There are ten to the I-don’t-know-what possible ways. That, by the way, is entropy. Entropy is how many microscopic possibilities there are for this given macroscopic state. Fine? That’s how entropy is defined. Or the log of it, never mind. That’s how entropy is defined. But there are many such possibilities. Fine? But what difference does it make? It’s not important at all. Because from the perspective of the Holy One, blessed be He, what He wants is that there be here a liquid with such-and-such properties. That’s what He needs. Now in order to produce such a liquid there’s no problem: you have to recruit lots and lots of molecules and mix them together, give them certain properties, and let them do what they are expected to do. So why should every such molecule need to have a role? It’s not interesting. If that’s not really the thing you’re looking for, then the micro language is only a basis for producing the macro. It’s not interesting at all. But without the micro there will be no macro. And it’s not that the Holy One, blessed be He, could have produced the macro without resorting to the micro. I don’t know—maybe yes, but apparently not; otherwise I assume He would have done so. Apparently not. And since that is so, fine, then that is the form for achieving the macro.

If I go back to peacocks: say I have a thousand peacocks. I need those peacocks here because of ecological considerations. Why should I care now what happens to each individual peacock? What difference does it make at all? As far as I’m concerned, treat this as one body called “a thousand peacocks.” That is one entity, and it is watched over, it has a role, everything is fine. After all, a peacock too contains many molecules. Why not look at each molecule of the peacock and ask what exactly it is doing? Because there it’s obvious to us that the peacock is meant for the purpose for which it is meant. So I’m saying: not the peacock—the totality of peacocks is meant for that purpose, and therefore there is no obstacle to there really being redundancy, a degree of freedom—that is, freedom in the small degrees of freedom, meaning in the micro.

And in that sense I think this explains exactly what Maimonides is saying here about providence over the species. Providence over the species is basically saying: the entity we are talking about, the relevant entity we are talking about, is the collective. It’s not at all—you are looking at a peacock as an entity. The peacock is not an entity. A thousand peacocks, the peacock population—that is the entity. Meaning, that’s what we need here, and that is what providence applies to. Human beings: the individual person is an entity. There is also the collective, but the individual person also has significance, and therefore—unlike the molecules that make him up—here too there are levels we ignore, right? After all, a person is also made up of molecules or cells. That’s not interesting, right? It’s not interesting which cell is where. Cells come and go; nobody cares about that. But there has to be a person who functions in a certain way. So even in a person there is a level of integration at which we begin. It’s just that for the individual human being, that already is a level of integration that interests the Holy One, blessed be He. But even he has sub-levels that are not of interest. And with peacocks, it’s the entire peacock population. There too, that’s the whole story.

I don’t think there is anything theologically problematic here. Actually, I wanted now to talk a bit—I see I’m not getting to it at all—I really wanted to talk a bit about the question of the relation between the individual person and the collective among human beings. Meaning, how to understand the relation between micro and macro in human beings, which of course is no longer directly connected to this topic. But apropos this Maimonides on providence over the species, maybe I’ll do that next time, and then we’ll continue.